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Journal articles on the topic 'Connectivité des graphes'

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Published: 26 July 2024

Last updated: 27 July 2024

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1

CLAUZEL, Céline, Christophe EGGERT, Simon TARABON, Lili PASQUET, Gilles VUIDEL, Marion BAILLEUL, Claude MIAUD, and Claire GODET. "Analyser la connectivité de la trame turquoise : définition, caractérisation et enjeux opérationnels." Sciences Eaux & Territoires, no. 43 (October 16, 2023): 67–71. http://dx.doi.org/10.20870/revue-set.2023.43.7642.

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Revue Sciences Eaux & Territoires - Vient de paraître en ligneLa fragmentation du paysage se matérialise par une rupture de connexion au sein des réseaux écologiques. Le concept de trame verte et bleue est apparu comme un outil de protection et de restauration des continuités écologiques dans les territoires. De nouvelles trames écologiques ont récemment été proposées pour identifier d’autres discontinuités écologiques effectives. C’est notamment le cas de la trame turquoise associant la trame bleue et la partie de la trame verte en interaction fonctionnelle. La trame turquoise regroupe ainsi différents types d’habitats aquatiques et terrestres dont dépendent de nombreuses espèces d’amphibiens, d’odonates et autres invertébrés ou encore de chiroptères. Cette nouvelle trame bénéficie d’une attention croissante dans le monde opérationnel, alors même que sa définition et les méthodes de caractérisation ne sont pas encore stabilisées. Cet article propose de contribuer à une meilleure définition et compréhension de la trame turquoise. S’appuyant sur la méthode des graphes paysagers, aujourd’hui largement utilisée pour modéliser les réseaux écologiques et mesurer leur connectivité, le projet INTERFACE a permis le développement d’un protocole innovant de réseau multi-habitats pour tenir compte de l’hétérogénéité des habitats dans l’évaluation de la connectivité de la trame turquoise. Il permet ainsi d’aller au-delà de la délimitation d’une zone tampon autour des cours d’eau et d'identifier les zones fonctionnelles à préserver, les zones vulnérables et les points de conflits où il serait intéressant de restaurer des habitats aquatiques et/ou terrestres pour améliorer les connectivités.

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2

Durand-Dubief, Françoise, Gabriel Kocevar, Claudio Stamile, Salem Hannoun, François Cotton, and Dominique Sappey-Marinier. "Analyse de la connectivité structurelle cérébrale par la théorie des graphes : une nouvelle caractérisation des formes cliniques de sclérose en plaques." Revue Neurologique 173 (March 2017): S124. http://dx.doi.org/10.1016/j.neurol.2017.01.216.

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3

Chawki, M. B., A. Verger, E. Klesse, T. Witjas, J. P. Azulay, A. Eusebio, and E. Guedj. "Étude TEP cérébrale des troubles du contrôle des impulsions dans la maladie de Parkinson : approche de la connectivité métabolique par théorie des graphes." Médecine Nucléaire 42, no. 3 (May 2018): 137. http://dx.doi.org/10.1016/j.mednuc.2018.03.015.

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4

Prajapati, Rajeshri, Amit Parikh, and Pradeep Jha. "Exploring Novel Edge Connectivity in Graph Theory and its Impact on Eulerian Line Graphs." International Journal of Science and Research (IJSR) 12, no. 11 (November 5, 2023): 1515–19. http://dx.doi.org/10.21275/sr231120155230.

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5

Kulli, V. R. "ATOM BOND CONNECTIVITY E-BANHATTI INDICES." INTERNATIONAL JOURNAL OF MATHEMATICS AND COMPUTER RESEARCH 11, no. 01 (January 30, 2023): 3201–8. http://dx.doi.org/10.47191/ijmcr/v11i1.13.

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In this paper, we introduce the atom bond connectivity E-Banhatti index and the sum atom bond connectivity E-Banhatti index of a graph. Also we compute these newly defined atom bond connectivity E-Banhatti indices for wheel graphs, friendship graphs, chain silicate networks, honeycomb networks and nanotubes.

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6

Zhao, Kewen. "A simple proof of Whitney's Theorem on connectivity in graphs." Mathematica Bohemica 136, no. 1 (2011): 25–26. http://dx.doi.org/10.21136/mb.2011.141446.

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7

Boronina, Anna, Vladimir Maksimenko, and Alexander E. Hramov. "Convolutional Neural Network Outperforms Graph Neural Network on the Spatially Variant Graph Data." Mathematics 11, no. 11 (May 30, 2023): 2515. http://dx.doi.org/10.3390/math11112515.

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Applying machine learning algorithms to graph-structured data has garnered significant attention in recent years due to the prevalence of inherent graph structures in real-life datasets. However, the direct application of traditional deep learning algorithms, such as Convolutional Neural Networks (CNNs), is limited as they are designed for regular Euclidean data like 2D grids and 1D sequences. In contrast, graph-structured data are in a non-Euclidean form. Graph Neural Networks (GNNs) are specifically designed to handle non-Euclidean data and make predictions based on connectivity rather than spatial structure. Real-life graph data can be broadly categorized into two types: spatially-invariant graphs, where the link structure between nodes is independent of their spatial positions, and spatially-variant graphs, where node positions provide additional information about the graph’s properties. However, there is limited understanding of the effect of spatial variance on the performance of Graph Neural Networks. In this study, we aim to address this issue by comparing the performance of GNNs and CNNs on spatially-variant and spatially-invariant graph data. In the case of spatially-variant graphs, when represented as adjacency matrices, they can exhibit Euclidean-like spatial structure. Based on this distinction, we hypothesize that CNNs may outperform GNNs when working with spatially-variant graphs, while GNNs may excel on spatially-invariant graphs. To test this hypothesis, we compared the performance of CNNs and GNNs under two scenarios: (i) graphs in the training and test sets had the same connectivity pattern and spatial structure, and (ii) graphs in the training and test sets had the same connectivity pattern but different spatial structures. Our results confirmed that the presence of spatial structure in a graph allows for the effective use of CNNs, which may even outperform GNNs. Thus, our study contributes to the understanding of the effect of spatial graph structure on the performance of machine learning methods and allows for the selection of an appropriate algorithm based on the spatial properties of the real-life graph dataset.

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8

Yalaniak Supriya Butte, Ashwini. "Neighbour Degree Connectivity Indices of Graphs and Its Applications to the Octane Isomers." International Journal of Science and Research (IJSR) 12, no. 4 (April 5, 2023): 1892–96. http://dx.doi.org/10.21275/sr23716144709.

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9

Jiang, Huiqin, and Yongsheng Rao. "Connectivity Index in Vague Graphs with Application in Construction." Discrete Dynamics in Nature and Society 2022 (February 15, 2022): 1–15. http://dx.doi.org/10.1155/2022/9082693.

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The vague graph (VG), which has recently gained a place in the family of fuzzy graph (FG), has shown good capabilities in the face of problems that cannot be expressed by fuzzy graphs and interval-valued fuzzy graphs. Connectivity index (CI) in graphs is a fundamental issue in fuzzy graph theory that has wide applications in the real world. The previous definitions’ limitations in the connectivity of fuzzy graphs directed us to offer new classifications in vague graph. Hence, in this paper, we investigate connectivity index, average connectivity index, and Randic index in vague graphs with several examples. Also, one of the motives of this research is to introduce some special types of vertices such as vague connectivity enhancing vertex, vague connectivity reducing vertex, and vague connectivity neutral vertex with their properties. Finally, an application of connectivity index in the selected town for building hospital is presented.

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10

Oellermann, Ortrud R. "Major n-connected graphs." Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics 47, no. 1 (August 1989): 43–52. http://dx.doi.org/10.1017/s1446788700031189.

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AbstractAn induced subgraph H of connectivity (edge-connectivity) n in a graph G is a major n-connected (major n-edge-connected) subgraph of G if H contains no subgraph with connectivity (edge- connectivity) exceeding n and H has maximum order with respect to this property. An induced subgraph is a major (major edge-) subgraph if it is a major n-connected (major n-edge-connected) subgraph for some n. Let m be the maximum order among all major subgraphs of C. Then the major connectivity set K(G) of G is defined as the set of all n for which there exists a major n-connected subgraph of G having order m. The major edge-connectivity set is defined analogously. The connectivity and the elements of the major connectivity set of a graph are compared, as are the elements of the major connectivity set and the major edge-connectivity set of a graph. It is shown that every set S of nonnegative integers is the major connectivity set of some graph G. Further, it is shown that for each positive integer m exceeding every element of S, there exists a graph G such that every major k-connected subgraph of G, where k ∈ K(G), has order m. Moreover, upper and lower bounds on the order of such graphs G are established.

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11

de Fraysseix, Hubert, and Patrice Ossona de Mendez. "Connectivity of Planar Graphs." Journal of Graph Algorithms and Applications 5, no. 5 (2001): 93–105. http://dx.doi.org/10.7155/jgaa.00041.

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12

Knor, Martin, and Ludovít Niepel. "Connectivity of path graphs." Discussiones Mathematicae Graph Theory 20, no. 2 (2000): 181. http://dx.doi.org/10.7151/dmgt.1118.

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13

Rhodes, F., and S. Wilson. "Connectivity of Knight's Graphs." Proceedings of the London Mathematical Society s3-67, no. 2 (September 1993): 225–42. http://dx.doi.org/10.1112/plms/s3-67.2.225.

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14

Jackson, Bill, and Tibor Jordánn. "Connectivity Augmentation of Graphs." Electronic Notes in Discrete Mathematics 5 (July 2000): 185–88. http://dx.doi.org/10.1016/s1571-0653(05)80158-1.

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15

Chávez-Domínguez, Javier Alejandro, and Andrew T. Swift. "Connectivity for quantum graphs." Linear Algebra and its Applications 608 (January 2021): 37–53. http://dx.doi.org/10.1016/j.laa.2020.08.020.

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16

Acer, Utku Günay, Petros Drineas, and Alhussein A. Abouzeid. "Connectivity in time-graphs." Pervasive and Mobile Computing 7, no. 2 (April 2011): 160–71. http://dx.doi.org/10.1016/j.pmcj.2010.11.011.

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17

Hager, Michael. "Path-connectivity in graphs." Discrete Mathematics 59, no. 1-2 (April 1986): 53–59. http://dx.doi.org/10.1016/0012-365x(86)90068-3.

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18

Currie, J. D. "Connectivity of distance graphs." Discrete Mathematics 103, no. 1 (May 1992): 91–94. http://dx.doi.org/10.1016/0012-365x(92)90042-e.

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19

Matsumoto, Naoki, and Tomoki Nakamigawa. "Game connectivity of graphs." Discrete Mathematics 343, no. 11 (November 2020): 112104. http://dx.doi.org/10.1016/j.disc.2020.112104.

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20

Boros, Endre, Pinar Heggernes, Pim van 't Hof, and Martin Milanič. "Vector connectivity in graphs." Networks 63, no. 4 (February 10, 2014): 277–85. http://dx.doi.org/10.1002/net.21545.

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21

Santra, Shyam Sundar, Prabhakaran Victor, Mahadevan Chandramouleeswaran, Rami Ahmad El-Nabulsi, Khaled Mohamed Khedher, and Vediyappan Govindan. "Connectivity of Semiring Valued Graphs." Symmetry 13, no. 7 (July 8, 2021): 1227. http://dx.doi.org/10.3390/sym13071227.

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Graph connectivity theory is important in network implementations, transportation, network routing and network tolerance, among other things. Separation edges and vertices refer to single points of failure in a network, and so they are often sought-after. Chandramouleeswaran et al. introduced the principle of semiring valued graphs, also known as S-valued symmetry graphs, in 2015. Since then, works on S-valued symmetry graphs such as vertex dominating set, edge dominating set, regularity, etc. have been done. However, the connectivity of S-valued graphs has not been studied. Motivated by this, in this paper, the concept of connectivity in S-valued graphs has been studied. We have introduced the term vertex S-connectivity and edge S-connectivity and arrived some results for connectivity of a complete S-valued symmetry graph, S-path and S-star. Unlike the graph theory, we have observed that the inequality for connectivity κ(G)≤κ′(G)≤δ(G) holds in the case of S-valued graphs only when there is a symmetry of the graph as seen in Examples 3–5.

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22

Basavanagoud, B., Veena R. Desai, and Shreekant Patil. "(β ,α)−Connectivity Index of Graphs." Applied Mathematics and Nonlinear Sciences 2, no. 1 (January 30, 2017): 21–30. http://dx.doi.org/10.21042/amns.2017.1.00003.

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AbstractLet Eβ (G) be the set of paths of length β in a graph G. For an integer β ≥ 1 and a real number α, the (β,α)-connectivity index is defined as$$\begin{array}{} \displaystyle ^\beta\chi_\alpha(G)=\sum \limits_{v_1v_2 \cdot \cdot \cdot v_{\beta+1}\in E_\beta(G)}(d_{G}(v_1)d_{G}(v_2)...d_{G}(v_{\beta+1}))^{\alpha}. \end{array}$$The (2,1)-connectivity index shows good correlation with acentric factor of an octane isomers. In this paper, we compute the (2, α)-connectivity index of certain class of graphs, present the upper and lower bounds for (2, α)-connectivity index in terms of number of vertices, number of edges and minimum vertex degree and determine the extremal graphs which achieve the bounds. Further, we compute the (2, α)-connectivity index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p,q], tadpole graphs, wheel graphs and ladder graphs.

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23

Ali, Akbar, Ivan Gutman, Izudin Redžepović, Jaya Percival Mazorodze, Abeer M. Albalahi, and Amjad E. Hamza. "On the Difference of Atom-Bond Sum-Connectivity and Atom-Bond-Connectivity Indices." MATCH – Communications in Mathematical and in Computer Chemistry 91, no. 3 (December 2023): 725–40. http://dx.doi.org/10.46793/match.91-3.725a.

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The atom-bond connectivity (ABC) index is one of the wellinvestigated degree-based topological indices. The atom-bond sumconnectivity (ABS) index is a modified version of the ABC index, which was introduced recently. The primary goal of the present paper is to investigate the difference between the aforementioned two indices, namely ABS − ABC. It is shown that the difference ABS − ABC is positive for all graphs of minimum degree at least 2 as well as for all line graphs of those graphs of order at least 5 that are different from the path and cycle graphs. By means of computer search, the difference ABS − ABC is also calculated for all trees of order at most 15.

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24

Kim, Jaehoon, and Suil O. "Average connectivity and average edge-connectivity in graphs." Discrete Mathematics 313, no. 20 (October 2013): 2232–38. http://dx.doi.org/10.1016/j.disc.2013.05.024.

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25

Li, Chunfang, Shangwei Lin, and Shengjia Li. "Structure connectivity and substructure connectivity of star graphs." Discrete Applied Mathematics 284 (September 2020): 472–80. http://dx.doi.org/10.1016/j.dam.2020.04.009.

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26

Akram, Muhammad, Sidra Sayed, and Florentin Smarandache. "Neutrosophic Incidence Graphs With Application." Axioms 7, no. 3 (July 18, 2018): 47. http://dx.doi.org/10.3390/axioms7030047.

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In this research study, we introduce the notion of single-valued neutrosophic incidence graphs. We describe certain concepts, including bridges, cut vertex and blocks in single-valued neutrosophic incidence graphs. We present some properties of single-valued neutrosophic incidence graphs. We discuss the edge-connectivity, vertex-connectivity and pair-connectivity in neutrosophic incidence graphs. We also deal with a mathematical model of the situation of illegal migration from Pakistan to Europe.

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27

Sebastian, Arya, John N. Mordeson, and Sunil Mathew. "Generalized Fuzzy Graph Connectivity Parameters with Application to Human Trafficking." Mathematics 8, no. 3 (March 16, 2020): 424. http://dx.doi.org/10.3390/math8030424.

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Graph models are fundamental in network theory. But normalization of weights are necessary to deal with large size networks like internet. Most of the research works available in the literature have been restricted to an algorithmic perspective alone. Not much have been studied theoretically on connectivity of normalized networks. Fuzzy graph theory answers to most of the problems in this area. Although the concept of connectivity in fuzzy graphs has been widely studied, one cannot find proper generalizations of connectivity parameters of unweighted graphs. Generalizations for some of the existing vertex and edge connectivity parameters in graphs are attempted in this article. New parameters are compared with the old ones and generalized values are calculated for some of the major classes like cycles and trees in fuzzy graphs. The existence of super fuzzy graphs with higher connectivity values are established for both old and new parameters. The new edge connectivity values for some wider classes of fuzzy graphs are also obtained. The generalizations bring substantial improvements in fuzzy graph clustering techniques and allow a smooth theoretical alignment. Apart from these, a new class of fuzzy graphs called generalized t-connected fuzzy graphs are studied. An algorithm for clustering the vertices of a fuzzy graph and an application related to human trafficking are also proposed.

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28

Shi, Xiaolong, Saeed Kosari, Saira Hameed, Abdul Ghafar Shah, and Samee Ullah. "Application of connectivity index of cubic fuzzy graphs for identification of danger zones of tsunami threat." PLOS ONE 19, no. 1 (January 30, 2024): e0297197. http://dx.doi.org/10.1371/journal.pone.0297197.

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Fuzzy graphs are very important when we are trying to understand and study complex systems with uncertain and not exact information. Among different types of fuzzy graphs, cubic fuzzy graphs are special due to their ability to represent the membership degree of both vertices and edges using intervals and fuzzy numbers, respectively. To figure out how things are connected in cubic fuzzy graphs, we need to know about cubic α−strong, cubic β−strong and cubic δ−weak edges. These concepts better help in making decisions, solving problems and analyzing things like transportation, social networks and communication systems. The applicability of connectivity and comprehension of cubic fuzzy graphs have urged us to discuss connectivity in the domain of cubic fuzzy graphs. In this paper, the terms partial cubic α−strong and partial cubic δ−weak edges are introduced for cubic fuzzy graphs. The bounds and exact expression of connectivity index for several cubic fuzzy graphs are estimated. The average connectivity index for cubic fuzzy graphs is also defined and some results pertaining to these concepts are proved in this paper. The results demonstrate that removing some vertices or edges may cause a change in the value of connectivity index or average connectivity index, but the change will not necessarily be related to both values. This paper also defines the concepts of partial cubic connectivity enhancing node and partial cubic connectivity reducing node and some related results are proved. Furthermore, the concepts of cubic α−strong, cubic β− strong, cubic δ−weak edge, partial cubic α−strong and partial cubic δ−weak edges are utilized to identify areas most affected by a tsunami resulting from an earthquake. Finally, the research findings are compared with the existing methods to demonstrate their suitability and creativity.

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29

Jiang, Guisheng, Guidong Yu, and Jinde Cao. "The Least Algebraic Connectivity of Graphs." Discrete Dynamics in Nature and Society 2015 (2015): 1–9. http://dx.doi.org/10.1155/2015/756960.

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The algebraic connectivity of a graph is defined as the second smallest eigenvalue of the Laplacian matrix of the graph, which is a parameter to measure how well a graph is connected. In this paper, we present two unique graphs whose algebraic connectivity attain the minimum among all graphs whose complements are trees, but not stars, and among all graphs whose complements are unicyclic graphs, but not stars adding one edge, respectively.

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30

Razi, Adeel, Mohamed L. Seghier, Yuan Zhou, Peter McColgan, Peter Zeidman, Hae-Jeong Park, Olaf Sporns, Geraint Rees, and Karl J. Friston. "Large-scale DCMs for resting-state fMRI." Network Neuroscience 1, no. 3 (October 2017): 222–41. http://dx.doi.org/10.1162/netn_a_00015.

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This paper considers the identification of large directed graphs for resting-state brain networks based on biophysical models of distributed neuronal activity, that is, effective connectivity. This identification can be contrasted with functional connectivity methods based on symmetric correlations that are ubiquitous in resting-state functional MRI (fMRI). We use spectral dynamic causal modeling (DCM) to invert large graphs comprising dozens of nodes or regions. The ensuing graphs are directed and weighted, hence providing a neurobiologically plausible characterization of connectivity in terms of excitatory and inhibitory coupling. Furthermore, we show that the use of Bayesian model reduction to discover the most likely sparse graph (or model) from a parent (e.g., fully connected) graph eschews the arbitrary thresholding often applied to large symmetric (functional connectivity) graphs. Using empirical fMRI data, we show that spectral DCM furnishes connectivity estimates on large graphs that correlate strongly with the estimates provided by stochastic DCM. Furthermore, we increase the efficiency of model inversion using functional connectivity modes to place prior constraints on effective connectivity. In other words, we use a small number of modes to finesse the potentially redundant parameterization of large DCMs. We show that spectral DCM—with functional connectivity priors—is ideally suited for directed graph theoretic analyses of resting-state fMRI. We envision that directed graphs will prove useful in understanding the psychopathology and pathophysiology of neurodegenerative and neurodevelopmental disorders. We will demonstrate the utility of large directed graphs in clinical populations in subsequent reports, using the procedures described in this paper.

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31

Ma, Jingjing. "Algorithm for Graph’s Connectivity Problem Based on DNA Origami." Journal of Nanoelectronics and Optoelectronics 16, no. 2 (February 1, 2021): 333–36. http://dx.doi.org/10.1166/jno.2021.2961.

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Based on DNA origami, an algorithm is proposed for Graph’s Connectivity problem via the self-assembly of DNA origami structures. The desired DNA origami structures can be constructed. These structures can encode the information of Graph’s vertices and edges, because these structures have sticky ends, so they can assemble to advanced structures representing the information of a graph via specific hybridization. Via strand displacement reaction and agarose gel electrophoresis, the vertices can be deleted and the graph’s connectivity can be tested one by one. This is a highly parallel method, and can reduce the complexity of Graph’s Connectivity problem greatly.

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32

Ibraheem, Muhammad, Ebenezer Bonyah, and Muhammad Javaid. "Sum-Connectivity Coindex of Graphs under Operations." Journal of Chemistry 2022 (April 14, 2022): 1–14. http://dx.doi.org/10.1155/2022/4523223.

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Topological indices or coindices are mathematical parameters which are widely used to investigate different properties of graphs. The operations on graphs play vital roles in the formation of new molecular graphs from the old ones. Let Γ be a graph we perform four operations which are S , R , Q , and T and obtained subdivisions type graphs such that S Γ , R Γ , Q Γ , and T Γ , respectively. Let Γ 1 and Γ 2 be two simple graphs; then, F -sum graph is defined by performing the Cartesian product on F Γ 1 and Γ 2 ; mathematically, it is denoted by Γ 1 + F Γ 2 , where F ∈ S , R , Q , T . In this article, we have calculated sum-connectivity coindex for F -sum graphs. At the end, we have illustrated the results for particular F -sum graphs with the help of a table consisting of numerical values.

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33

Luo, Zuwen, and Liqiong Xu. "A Kind Of Conditional Vertex Connectivity Of Cayley Graphs Generated By Wheel Graphs." Computer Journal 63, no. 9 (November 13, 2019): 1372–84. http://dx.doi.org/10.1093/comjnl/bxz077.

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Abstract Let $G=(V(G), E(G))$ be a connected graph. A subset $T \subseteq V(G)$ is called an $R^{k}$-vertex-cut, if $G-T$ is disconnected and each vertex in $V(G)-T$ has at least $k$ neighbors in $G-T$. The cardinality of a minimum $R^{k}$-vertex-cut is the $R^{k}$-vertex-connectivity of $G$ and is denoted by $\kappa ^{k}(G)$. $R^{k}$-vertex-connectivity is a new measure to study the fault tolerance of network structures beyond connectivity. In this paper, we study $R^{1}$-vertex-connectivity and $R^{2}$-vertex-connectivity of Cayley graphs generated by wheel graphs, which are denoted by $AW_{n}$, and show that $\kappa ^{1}(AW_{n})=4n-7$ for $n\geq 6$; $\kappa ^{2}(AW_{n})=6n-12$ for $n\geq 6$.

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34

Ali, Akbar. "An alternative but short proof of a result of Zhu and Lu concerning general sum-connectivity index." Asian-European Journal of Mathematics 11, no. 02 (March 19, 2018): 1850030. http://dx.doi.org/10.1142/s1793557118500304.

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Recently, Zhu and Lu, [On the general sum-connectivity index of tricyclic graphs, J. Appl. Math. Comput. 51(1) (2016) 177–188] determined the graphs having maximum general sum-connectivity index among all [Formula: see text]-vertex tricyclic graphs. In this short note, an alternative but considerable short approach is proposed for determining the aforementioned graphs.

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35

Binu, M., Sunil Mathew, and J. N. Mordeson. "Connectivity status of fuzzy graphs." Information Sciences 573 (September 2021): 382–95. http://dx.doi.org/10.1016/j.ins.2021.05.068.

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36

Liu, Runrun, Martin Rolek, D. Christopher Stephens, Dong Ye, and Gexin Yu. "Connectivity for Kite-Linked Graphs." SIAM Journal on Discrete Mathematics 35, no. 1 (January 2021): 431–46. http://dx.doi.org/10.1137/19m130282x.

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37

Matsumoto, Naoki, and Tomoki Nakamigawa. "Game edge-connectivity of graphs." Discrete Applied Mathematics 298 (July 2021): 155–64. http://dx.doi.org/10.1016/j.dam.2021.04.005.

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38

Mathew, Sunil, and M. S. Sunitha. "Cycle connectivity in weighted graphs." Proyecciones (Antofagasta) 30, no. 1 (2011): 1–17. http://dx.doi.org/10.4067/s0716-09172011000100001.

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39

Mathew, Sunil, and M. S. Sunitha. "Cycle connectivity in fuzzy graphs." Journal of Intelligent & Fuzzy Systems 24, no. 3 (2013): 549–54. http://dx.doi.org/10.3233/ifs-2012-0573.

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40

Jin, Zemin, Xueliang Li, and Kaijun Wang. "The Monochromatic Connectivity of Graphs." Taiwanese Journal of Mathematics 24, no. 4 (August 2020): 785–815. http://dx.doi.org/10.11650/tjm/200102.

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41

Liu, Hongjuan, and Honghai Li. "Normalized algebraic connectivity of graphs." Discrete Mathematics, Algorithms and Applications 11, no. 03 (June 2019): 1950031. http://dx.doi.org/10.1142/s1793830919500319.

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Let [Formula: see text] be the second smallest normalized Laplacian eigenvalue of a graph [Formula: see text], called the normalized algebraic connectivity of [Formula: see text]. In this paper, we study the relation between the normalized algebraic connectivity of the coalescence of two graphs and that of these two graphs. Furthermore, we investigate how the normalized algebraic connectivity behaves when the graph is perturbed by relocating pendent edges.

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Caporossi, Gilles, Ivan Gutman, Pierre Hansen, and Ljiljana Pavlović. "Graphs with maximum connectivity index." Computational Biology and Chemistry 27, no. 1 (February 2003): 85–90. http://dx.doi.org/10.1016/s0097-8485(02)00016-5.

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Knor, Martin, and L'udovı́t Niepel. "Connectivity of iterated line graphs." Discrete Applied Mathematics 125, no. 2-3 (February 2003): 255–66. http://dx.doi.org/10.1016/s0166-218x(02)00197-x.

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Erdös, P., and J. W. Kennedy. "k-Connectivity in Random Graphs." European Journal of Combinatorics 8, no. 3 (July 1987): 281–86. http://dx.doi.org/10.1016/s0195-6698(87)80032-x.

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Uchizawa, Kei, Takanori Aoki, Takehiro Ito, and Xiao Zhou. "Generalized rainbow connectivity of graphs." Theoretical Computer Science 555 (October 2014): 35–42. http://dx.doi.org/10.1016/j.tcs.2014.01.007.

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Lai, Hong-Jian, Rui Xu, and Ju Zhou. "On Group Connectivity of Graphs." Graphs and Combinatorics 24, no. 3 (June 2008): 195–203. http://dx.doi.org/10.1007/s00373-008-0780-1.

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Li, Liangchen, Xiangwen Li, and Chi Shu. "Group Connectivity of Bridged Graphs." Graphs and Combinatorics 29, no. 4 (March 14, 2012): 1059–66. http://dx.doi.org/10.1007/s00373-012-1154-2.

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Leaños, J., and A. L. Trujillo-Negrete. "The Connectivity of Token Graphs." Graphs and Combinatorics 34, no. 4 (June 19, 2018): 777–90. http://dx.doi.org/10.1007/s00373-018-1913-9.

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Wu, Chai Wah. "Algebraic connectivity of directed graphs." Linear and Multilinear Algebra 53, no. 3 (June 2005): 203–23. http://dx.doi.org/10.1080/03081080500054810.

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Amer, Rafael, and Jos� Miguel Gim�nez. "A connectivity game for graphs." Mathematical Methods of Operational Research 60, no. 3 (December 2004): 453–70. http://dx.doi.org/10.1007/s001860400356.

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