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Статті в журналах з теми "Generalized graphs"

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Автор: Grafiati

Опубліковано: 8 червня 2024

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1

Sedláček, Jiří. "On generalized outerplanarity of line graphs." Časopis pro pěstování matematiky 115, no. 3 (1990): 273–77. http://dx.doi.org/10.21136/cpm.1990.118405.

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2

Samanta, Sovan, and Biswajit Sarkar. "Generalized fuzzy Euler graphs and generalized fuzzy Hamiltonian graphs." Journal of Intelligent & Fuzzy Systems 35, no. 3 (October 1, 2018): 3413–19. http://dx.doi.org/10.3233/jifs-17322.

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3

Das, Angsuman, Sucharita Biswas, and Manideepa Saha. "Generalized Andrásfai Graphs." Discussiones Mathematicae - General Algebra and Applications 42, no. 2 (2022): 449. http://dx.doi.org/10.7151/dmgaa.1401.

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4

Marušič, Dragan, Raffaele Scapellato, and Norma Zagaglia Salvi. "Generalized Cayley graphs." Discrete Mathematics 102, no. 3 (May 1992): 279–85. http://dx.doi.org/10.1016/0012-365x(92)90121-u.

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5

Zverovich, Igor E. "Generalized Matrogenic Graphs." Annals of Combinatorics 10, no. 2 (September 2006): 285–90. http://dx.doi.org/10.1007/s00026-006-0288-4.

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6

Lovász, László, and Vera T. Sós. "Generalized quasirandom graphs." Journal of Combinatorial Theory, Series B 98, no. 1 (January 2008): 146–63. http://dx.doi.org/10.1016/j.jctb.2007.06.005.

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7

Brand, Neal, and Margaret Morton. "Generalized steinhaus graphs." Journal of Graph Theory 20, no. 1 (August 1995): 47–58. http://dx.doi.org/10.1002/jgt.3190200105.

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8

Alon, Noga, and Edward R. Scheinerman. "Generalized sum graphs." Graphs and Combinatorics 8, no. 1 (March 1992): 23–29. http://dx.doi.org/10.1007/bf01271705.

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9

IRSİC, VESNA, SANDI KLAVZAR, and ELİF TAN. "Generalized Pell graphs." Turkish Journal of Mathematics 47, no. 7 (November 9, 2023): 1955–73. http://dx.doi.org/10.55730/1300-0098.3475.

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10

Limaye, N. B., and Mulupuri Shanthi C. Rao. "On $2$-extendability of generalized Petersen graphs." Mathematica Bohemica 121, no. 1 (1996): 77–81. http://dx.doi.org/10.21136/mb.1996.125939.

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11

Luo, Ricai, Khadija Dawood, Muhammad Kamran Jamil, and Muhammad Azeem. "Some new results on the face index of certain polycyclic chemical networks." Mathematical Biosciences and Engineering 20, no. 5 (2023): 8031–48. http://dx.doi.org/10.3934/mbe.2023348.

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Анотація:

<abstract><p>Silicate minerals make up the majority of the earth's crust and account for almost 92 percent of the total. Silicate sheets, often known as silicate networks, are characterised as definite connectivity parallel designs. A key idea in studying different generalised classes of graphs in terms of planarity is the face of the graph. It plays a significant role in the embedding of graphs as well. Face index is a recently created parameter that is based on the data from a graph's faces. The current draft is utilizing a newly established face index, to study different silicate networks. It consists of a generalized chain of silicate, silicate sheet, silicate network, carbon sheet, polyhedron generalized sheet, and also triangular honeycomb network. This study will help to understand the structural properties of chemical networks because the face index is more generalized than vertex degree based topological descriptors.</p></abstract>

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12

Sirisuk, Siripong, and Yotsanan Meemark. "Generalized symplectic graphs and generalized orthogonal graphs over finite commutative rings." Linear and Multilinear Algebra 67, no. 12 (July 24, 2018): 2427–50. http://dx.doi.org/10.1080/03081087.2018.1494124.

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13

Sun, Daoqiang, Zhengying Zhao, Xiaoxiao Li, Jiayi Cao, and Yu Yang. "On Subtree Number Index of Generalized Book Graphs, Fan Graphs, and Wheel Graphs." Journal of Mathematics 2021 (April 9, 2021): 1–15. http://dx.doi.org/10.1155/2021/5511214.

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Анотація:

With generating function and structural analysis, this paper presents the subtree generating functions and the subtree number index of generalized book graphs, generalized fan graphs, and generalized wheel graphs, respectively. As an application, this paper also briefly studies the subtree number index and the asymptotic properties of the subtree densities in regular book graphs, regular fan graphs, and regular wheel graphs. The results provide the basis for studying novel structural properties of the graphs generated by generalized book graphs, fan graphs, and wheel graphs from the perspective of the subtree number index.

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14

Heidari, Dariush, and Bijan Davvaz. "Graph product of generalized Cayley graphs over polygroups." Algebraic structures and their applications 6, no. 1 (April 1, 2019): 49–56. http://dx.doi.org/10.29252/asta.6.1.49.

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15

Nedela, Roman, and Martin Škoviera. "Which generalized petersen graphs are cayley graphs?" Journal of Graph Theory 19, no. 1 (January 1995): 1–11. http://dx.doi.org/10.1002/jgt.3190190102.

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16

Malyshev, Fedor M. "Generalized de Bruijn graphs." Discrete Mathematics and Applications 32, no. 1 (February 1, 2022): 11–38. http://dx.doi.org/10.1515/dma-2022-0002.

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Abstract We study the graphs of transitions between states of nonautonomous automata that provide, with independent equiprobable input signs, an equiprobable distribution on the set of all states in the minimum possible number of cycles, as is the case of the de Bruijn graphs corresponding to shift registers. It is proved that in the case of a binary input alphabet, there are at least 12r−33 pairwise nonisomorphic directed graphs with 2 r vertices that have this property. All graphs of this type with 8 and 9 vertices are found.

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17

Yaguchi, Makoto. "A GENERALIZED FRAMEWORK FOR LISTING CUTS AND GRAPHS." Journal of the Operations Research Society of Japan 57, no. 2 (2014): 75–86. http://dx.doi.org/10.15807/jorsj.57.75.

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18

ARRIGHI, PABLO, SIMON MARTIEL, and VINCENT NESME. "Cellular automata over generalized Cayley graphs." Mathematical Structures in Computer Science 28, no. 3 (May 29, 2017): 340–83. http://dx.doi.org/10.1017/s0960129517000044.

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Анотація:

It is well-known that cellular automata can be characterized as the set of translation-invariant continuous functions over a compact metric space; this point of view makes it easy to extend their definition from grids to Cayley graphs. Cayley graphs have a number of useful features: the ability to graphically represent finitely generated group elements and their relations; to name all vertices relative to an origin; and the fact that they have a well-defined notion of translation. We propose a notion of graphs, which preserves or generalizes these features. Whereas Cayley graphs are very regular, generalized Cayley graphs are arbitrary, although of a bounded degree. We extend cellular automata theory to these arbitrary, bounded degree, time-varying graphs. The obtained notion of cellular automata is stable under composition and under inversion.

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19

Imrich, Wilfried, and Iztok Peterin. "Recognizing generalized Sierpiński graphs." Applicable Analysis and Discrete Mathematics 14, no. 1 (2020): 122–37. http://dx.doi.org/10.2298/aadm180331003i.

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Let H be an arbitrary graph with vertex set V (H) = [nH] = {l,?, nH}. The generalized Sierpi?ski graph SnH , n ? N, is defined on the vertex set [nH]n, two different vertices u = un ?u1 and v = vn ? v1 being adjacent if there exists an h? [n] such that (a) ut = vt, for t > h, (b) uh ? vh and uhvh ? E(H), and (c) ut = vh and vt = uh for t < h. If H is the complete graph Kk, then we speak of the Sierpi?ski graph Sn k . We present an algorithm that recognizes Sierpi?ski graphs Sn k in O(|V (Sn k )|1+1=n) = O(|E(Sn k )|) time. For generalized Sierpi?ski graphs SnH we present a polynomial time algorithm for the case when H belong to a certain well defined class of graphs. We also describe how to derive the base graph H from an arbitrarily given SnH .

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20

Ivančo, Jaroslav. "Supermagic generalized double graphs." Discussiones Mathematicae Graph Theory 36, no. 1 (2016): 211. http://dx.doi.org/10.7151/dmgt.1849.

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21

Avart, Christian, Tomasz Łuczak, and Vojtěch Rödl. "On generalized shift graphs." Fundamenta Mathematicae 226, no. 2 (2014): 173–99. http://dx.doi.org/10.4064/fm226-2-6.

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22

Mooney, Christopher Park. "Generalized Irreducible Divisor Graphs." Communications in Algebra 42, no. 10 (May 14, 2014): 4366–75. http://dx.doi.org/10.1080/00927872.2013.811246.

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23

Hell, Pavol, Sulamita Klein, Fabio Protti, and Loana Tito. "On generalized split graphs." Electronic Notes in Discrete Mathematics 7 (April 2001): 98–101. http://dx.doi.org/10.1016/s1571-0653(04)00234-3.

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24

Kooij, Robert. "On generalized windmill graphs." Linear Algebra and its Applications 565 (March 2019): 25–46. http://dx.doi.org/10.1016/j.laa.2018.11.025.

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25

Shyue-Ming Tang, Yue-Li Wang, and Chien-Yi Li. "Generalized Recursive Circulant Graphs." IEEE Transactions on Parallel and Distributed Systems 23, no. 1 (January 2012): 87–93. http://dx.doi.org/10.1109/tpds.2011.109.

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26

MacGillivray, Gary, and Min-Li Yu. "Generalized partitions of graphs." Discrete Applied Mathematics 91, no. 1-3 (January 1999): 143–53. http://dx.doi.org/10.1016/s0166-218x(98)00124-3.

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27

Wang, Shou-Zhong, and Rong Si Chen. "Regular generalized polyomino graphs." Journal of Mathematical Chemistry 42, no. 4 (November 2, 2006): 957–67. http://dx.doi.org/10.1007/s10910-006-9152-3.

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28

Gharat, Pritam M., Uday P. Khedker, and Alan Mycroft. "Generalized Points-to Graphs." ACM Transactions on Programming Languages and Systems 42, no. 2 (May 27, 2020): 1–78. http://dx.doi.org/10.1145/3382092.

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29

Suohai, Fan. "Generalized symmetry of graphs." Electronic Notes in Discrete Mathematics 23 (November 2005): 51–60. http://dx.doi.org/10.1016/j.endm.2005.07.079.

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30

Malyshev, F. M., and V. E. Tarakanov. "Generalized de Bruijn graphs." Mathematical Notes 62, no. 4 (October 1997): 449–56. http://dx.doi.org/10.1007/bf02358978.

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31

K Pranavan, H. P. Patil. "On the Minimally Non-outerplanarity of Generalized Middle and Total Graphs." Mapana - Journal of Sciences 12, no. 3 (July 1, 2013): 1–8. http://dx.doi.org/10.12723/mjs.26.4.

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Анотація:

Systo and Topp introduced the notions of generalized line, middle and total graphs and they studied the planarity and outerplanarity of these classes of graphs. Conditions under which generalized middle graphs and generalized total graphs are minimally non-outerplanar are discussed in this paper. Keywords : Planar graphs, middle graphs, total graphs, regular graphs, cocktail party graphs, cliques, cutvertices. 1. Introduction Let

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32

Zitnik, Arjana, Boris Horvat, and Tomaz Pisanski. "ALL GENERALIZED PETERSEN GRAPHS ARE UNIT-DISTANCE GRAPHS." Journal of the Korean Mathematical Society 49, no. 3 (May 1, 2012): 475–91. http://dx.doi.org/10.4134/jkms.2012.49.3.475.

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33

Day, Khaled, and Anand Tripathi. "Arrangement graphs: a class of generalized star graphs." Information Processing Letters 42, no. 5 (July 1992): 235–41. http://dx.doi.org/10.1016/0020-0190(92)90030-y.

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34

Chia, Gek Ling, and Chan Lye Lee. "Skewness of generalized Petersen graphs and related graphs." Frontiers of Mathematics in China 7, no. 3 (February 17, 2012): 427–36. http://dx.doi.org/10.1007/s11464-012-0186-5.

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35

Bonato, Anthony, Peter J. Cameron, Dejan Delić, and Stéphan Thomassé. "Generalized Pigeonhole Properties of Graphs and Oriented Graphs." European Journal of Combinatorics 23, no. 3 (April 2002): 257–74. http://dx.doi.org/10.1006/eujc.2002.0574.

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36

Chen, Jing, Xu Yang, and Xiaomin Zhu. "Isomorphisms and Automorphisms of Generalized Semi-Cayley Graphs." Algebra Colloquium 26, no. 02 (May 7, 2019): 321–28. http://dx.doi.org/10.1142/s1005386719000245.

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Анотація:

In this paper we propose the concept of generalized semi-Cayley graphs, which is a combination of semi-Cayley graphs and generalized Cayley graphs. We study the isomorphisms and automorphisms of generalized semi-Cayley graphs and other related properties.

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37

Zhuang, Jun, and Mohammad Al Hasan. "Defending Graph Convolutional Networks against Dynamic Graph Perturbations via Bayesian Self-Supervision." Proceedings of the AAAI Conference on Artificial Intelligence 36, no. 4 (June 28, 2022): 4405–13. http://dx.doi.org/10.1609/aaai.v36i4.20362.

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Анотація:

In recent years, plentiful evidence illustrates that Graph Convolutional Networks (GCNs) achieve extraordinary accomplishments on the node classification task. However, GCNs may be vulnerable to adversarial attacks on label-scarce dynamic graphs. Many existing works aim to strengthen the robustness of GCNs; for instance, adversarial training is used to shield GCNs against malicious perturbations. However, these works fail on dynamic graphs for which label scarcity is a pressing issue. To overcome label scarcity, self-training attempts to iteratively assign pseudo-labels to highly confident unlabeled nodes but such attempts may suffer serious degradation under dynamic graph perturbations. In this paper, we generalize noisy supervision as a kind of self-supervised learning method and then propose a novel Bayesian self-supervision model, namely GraphSS, to address the issue. Extensive experiments demonstrate that GraphSS can not only affirmatively alert the perturbations on dynamic graphs but also effectively recover the prediction of a node classifier when the graph is under such perturbations. These two advantages prove to be generalized over three classic GCNs across five public graph datasets.

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38

Cáceres, José, and Alberto Márquez. "A linear algorithm to recognize maximal generalized outerplanar graphs." Mathematica Bohemica 122, no. 3 (1997): 225–30. http://dx.doi.org/10.21136/mb.1997.126148.

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39

Javaid, Muhammad, Saira Javed, Saima Q. Memon, and Abdulaziz Mohammed Alanazi. "Forgotten Index of Generalized Operations on Graphs." Journal of Chemistry 2021 (May 3, 2021): 1–14. http://dx.doi.org/10.1155/2021/9971277.

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Анотація:

In theoretical chemistry, several distance-based, degree-based, and counting polynomial-related topological indices (TIs) are used to investigate the different chemical and structural properties of the molecular graphs. Furtula and Gutman redefined the F -index as the sum of cubes of degrees of the vertices of the molecular graphs to study the different properties of their structure-dependency. In this paper, we compute F -index of generalized sum graphs in terms of various TIs of their factor graphs, where generalized sum graphs are obtained by using four generalized subdivision-related operations and the strong product of graphs. We have analyzed our results through the numerical tables and the graphical presentations for the particular generalized sum graphs constructed with the help of path (alkane) graphs.

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40

Pleanmani, Nopparat, and Sayan Panma. "On generalized composed properties of generalized product graphs." Indonesian Journal of Combinatorics 6, no. 2 (December 31, 2022): 130. http://dx.doi.org/10.19184/ijc.2022.6.2.5.

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<p>A property ℘ is defined to be a nonempty isomorphism-closed subclass of the class of all finite simple graphs. A nonempty set <em>S</em> of vertices of a graph <em>G</em> is said to be a ℘-set of <em>G</em> if <em>G</em>[<em>S</em>]∈ ℘. The maximum and minimum cardinalities of a ℘-set of <em>G</em> are denoted by <em>M</em><sub>℘</sub>(<em>G</em>) and <em>m</em><sub>℘</sub>(<em>G</em>), respectively. If <em>S</em> is a ℘-set such that its cardinality equals <em>M</em><sub>℘</sub>(<em>G</em>) or <em>m</em><sub>℘</sub>(<em>G</em>), we say that <em>S</em> is an <em>M</em><sub>℘</sub>-set or an <em>m</em><sub>℘</sub>-set of <em>G</em>, respectively. In this paper, we not only define six types of property ℘ by the using concepts of graph product and generalized graph product, but we also obtain <em>M</em><sub>℘</sub> and <em>m</em><sub>℘</sub> of product graphs in each type and characterize its <em>M</em><sub>℘</sub>-set.</p>

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41

Li, Yipeng, Jing Zhang, and Meili Wang. "The Square of Some Generalized Hamming Graphs." Mathematics 11, no. 11 (May 28, 2023): 2487. http://dx.doi.org/10.3390/math11112487.

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Анотація:

In this paper, we study the square of generalized Hamming graphs by the properties of abelian groups, and characterize some isomorphisms between the square of generalized Hamming graphs and the non-complete extended p-sum of complete graphs. As applications, we determine the eigenvalues of the square of some generalized Hamming graphs.

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42

Subbulakshmi, M., and I. Valliammal. "DECOMPOSITION OF GENERALIZED FAN GRAPHS." Advances in Mathematics: Scientific Journal 10, no. 5 (May 5, 2021): 2381–92. http://dx.doi.org/10.37418/amsj.10.5.7.

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Let $G=(V,E)$ be a finite graph. The Generalized Fan Graph $F_{m,n}$ is defined as the graph join $\overline{K_m}+P_n$, where $\overline{K_m}$ is the empty graph on $m$ vertices and $P_n$ is the path graph on $n$ vertices. Decomposition of Generalized Fan Graph denoted by $D(F_{m,n})$. A star with $3$ edges is called a claw $S_3$. In this paper, we discuss the decomposition of Generalized Fan Graph into claws, cycles and paths.

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43

Borowiecki, Mieczysław, Ewa Drgas-Burchardt, and Peter Mihók. "Generalized list colourings of graphs." Discussiones Mathematicae Graph Theory 15, no. 2 (1995): 185. http://dx.doi.org/10.7151/dmgt.1016.

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44

Borowiecki, Mieczysław, Arnfried Kemnitz, Massimiliano Marangio, and Peter Mihók. "Generalized total colorings of graphs." Discussiones Mathematicae Graph Theory 31, no. 2 (2011): 209. http://dx.doi.org/10.7151/dmgt.1540.

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45

Mihók, Peter, Janka Oravcová, and Roman Soták. "Generalized circular colouring of graphs." Discussiones Mathematicae Graph Theory 31, no. 2 (2011): 345. http://dx.doi.org/10.7151/dmgt.1550.

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46

Estrada-Moreno, Alejandro, Juan Alberto Rodríguez-Velázquez, and Erick D. Rodríquez-Bazan. "On generalized Sierpi\'nski graphs." Discussiones Mathematicae Graph Theory 37, no. 3 (2017): 547. http://dx.doi.org/10.7151/dmgt.1945.

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47

Yang, Xu, Weijun Liu, and Lihua Feng. "Isomorphisms of generalized Cayley graphs." Ars Mathematica Contemporanea 15, no. 2 (August 12, 2018): 407–24. http://dx.doi.org/10.26493/1855-3974.1345.ae6.

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48

Liu, Shunyi. "Generalized Permanental Polynomials of Graphs." Symmetry 11, no. 2 (February 16, 2019): 242. http://dx.doi.org/10.3390/sym11020242.

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Анотація:

The search for complete graph invariants is an important problem in graph theory and computer science. Two networks with a different structure can be distinguished from each other by complete graph invariants. In order to find a complete graph invariant, we introduce the generalized permanental polynomials of graphs. Let G be a graph with adjacency matrix A ( G ) and degree matrix D ( G ) . The generalized permanental polynomial of G is defined by P G ( x , μ ) = per ( x I − ( A ( G ) − μ D ( G ) ) ) . In this paper, we compute the generalized permanental polynomials for all graphs on at most 10 vertices, and we count the numbers of such graphs for which there is another graph with the same generalized permanental polynomial. The present data show that the generalized permanental polynomial is quite efficient for distinguishing graphs. Furthermore, we can write P G ( x , μ ) in the coefficient form ∑ i = 0 n c μ i ( G ) x n − i and obtain the combinatorial expressions for the first five coefficients c μ i ( G ) ( i = 0 , 1 , ⋯ , 4 ) of P G ( x , μ ) .

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49

Zelinka, Bohdan. "Domination in generalized Petersen graphs." Czechoslovak Mathematical Journal 52, no. 1 (March 2002): 11–16. http://dx.doi.org/10.1023/a:1021759001873.

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50

Varkey T.K, Mathew, and Sreena T.D. "Fuzzification of Generalized Petersen Graphs." International Journal of Mathematics Trends and Technology 54, no. 2 (February 25, 2018): 133–37. http://dx.doi.org/10.14445/22315373/ijmtt-v54p514.

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