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1

Hamidi, M. "Zero Divisor Graphs Based on General Hyperrings‎." Journal of Algebraic Hyperstructures and Logical Algebras 4, no. 2 (2023): 131–49. http://dx.doi.org/10.61838/kman.jahla.4.2.9.

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This paper introduces the concepts of reproduced general hyperring and valued-orderable general hyperring and investigates some properties of these classes of general hyperrings‎. ‎It presents the notions of‎ ‎zero divisors and zero divisor graphs are founded on the absorbing elements of general hyperrings‎. ‎General hyperrings can have more than one zeroing element‎, ‎and therefore‎, ‎based on the zeroing elements‎, ‎multiple zero divisors can be obtained‎. ‎In this study‎, ‎we discuss the isomorphism of zero divisor graphs based on the diversity of divisors of zero divisors‎. ‎The non-empty intersection of the set of absorbing elements and the hyperproduct of zero divisors of general hyperrings play a major role in the production of zero divisor graphs‎. ‎Indeed it investigated a type classification of zero divisor graphs based on the finite general hyperrings‎. ‎We discuss the finite reproduced general hyperrings‎, ‎investigate their zero divisor graphs‎, ‎and show that an infinite reproduced general hyperring can have a finite zero divisor graph‎.
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2

FÜRER, MARTIN, and SHIVA PRASAD KASIVISWANATHAN. "Approximately Counting Embeddings into Random Graphs." Combinatorics, Probability and Computing 23, no. 6 (July 9, 2014): 1028–56. http://dx.doi.org/10.1017/s0963548314000339.

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LetHbe a graph, and letCH(G) be the number of (subgraph isomorphic) copies ofHcontained in a graphG. We investigate the fundamental problem of estimatingCH(G). Previous results cover only a few specific instances of this general problem, for example the case whenHhas degree at most one (the monomer-dimer problem). In this paper we present the first general subcase of the subgraph isomorphism counting problem, which is almost always efficiently approximable. The results rely on a new graph decomposition technique. Informally, the decomposition is a labelling of the vertices such that every edge is between vertices with different labels, and for every vertex all neighbours with a higher label have identical labels. The labelling implicitly generates a sequence of bipartite graphs, which permits us to break the problem of counting embeddings of large subgraphs into that of counting embeddings of small subgraphs. Using this method, we present a simple randomized algorithm for the counting problem. For all decomposable graphsHand all graphsG, the algorithm is an unbiased estimator. Furthermore, for all graphsHhaving a decomposition where each of the bipartite graphs generated is small and almost all graphsG, the algorithm is a fully polynomial randomized approximation scheme.We show that the graph classes ofHfor which we obtain a fully polynomial randomized approximation scheme for almost allGincludes graphs of degree at most two, bounded-degree forests, bounded-width grid graphs, subdivision of bounded-degree graphs, and major subclasses of outerplanar graphs, series-parallel graphs and planar graphs of large girth, whereas unbounded-width grid graphs are excluded. Moreover, our general technique can easily be applied to proving many more similar results.
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3

Shukur, Ali A., Akbar Jahanbani, and Haider Shelash. "The Behavior of Weighted Graph’s Orbit and Its Energy." Mathematical Problems in Engineering 2021 (May 17, 2021): 1–6. http://dx.doi.org/10.1155/2021/9933072.

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Studying the orbit of an element in a discrete dynamical system is one of the most important areas in pure and applied mathematics. It is well known that each graph contains a finite (or infinite) number of elements. In this work, we introduce a new analytical phenomenon to the weighted graphs by studying the orbit of their elements. Studying the weighted graph's orbit allows us to have a better understanding to the behaviour of the systems (graphs) during determined time and environment. Moreover, the energy of the graph’s orbit is given.
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4

Lakshmanan S., Aparna, S. B. Rao, and A. Vijayakumar. "Gallai and anti-Gallai graphs of a graph." Mathematica Bohemica 132, no. 1 (2007): 43–54. http://dx.doi.org/10.21136/mb.2007.133996.

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5

Kaviya, S., G. Mahadevan, and C. Sivagnanam. "Generalizing TCCD-Number For Power Graph Of Some Graphs." Indian Journal Of Science And Technology 17, SPI1 (April 25, 2024): 115–23. http://dx.doi.org/10.17485/ijst/v17sp1.243.

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Objective: Finding the triple connected certified domination number for the power graph of some peculiar graphs. Methods: A dominating set with the condition that every vertex in has either zero or at least two neighbors in and is triple connected is a called triple connected certified domination number of a graph. The minimum cardinality among all the triple connected certified dominating sets is called the triple connected certified domination number and is denoted by . The upper bound and lower bound of for the given graphs is found and then proved the upper bound and lower bound of were equal. Findings: We found the (TCCD)-number for the power graph of some peculiar graphs. Also, we have generalized the result for path, cycle, ladder graph, comb graph, coconut tree graph, triangular snake, alternate triangular snake, quadrilateral snake and tadpole graph. Novelty: The triple connected certified domination is a new parameter in which the certified domination holds the triple connected in induced . Keywords: Domination Number, Power Graphs, Triple Connected, Certified Domination, Triple Connected Certified Domination
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6

Srinivasan, Sakunthala, and Vimala Shanmugavel. "Comparative Study on Different Types of Energies." Indian Journal Of Science And Technology 17, no. 28 (July 31, 2024): 2954–59. http://dx.doi.org/10.17485/ijst/v17i28.1447.

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Objectives : The absolute sum of the eigenvalues is the definition of the graph's energy. In addition to discussing their relationship, this study compares the energy of the Adjacency matrix, Laplacian matrix, Signless Laplacian matrix, and Seidel matrix applied to ten distinct kinds of graphs. In this study, a correlation is established between the energy of graphs and the energy of Edge Antimagic graphs. Methods: The technical description of the graph's energy, . An Edge Antimagic graph's energy, identified by (G) = , is the absolute total of its eigenvalues. Findings: The energy was calculated along with its link to the energy of Edge Antimagic matrix, Adjacency matrix, Laplacian matrix, Signless Laplacian matrix, and Seidel matrix. Novelty: Edge antimagic graphs have been applied using the concept of energy. The energy of Edge Antimagic graphs and the energy of graphs were discovered to be related. An analysis was conducted comparing Adjacency energy, Seidel energy, Laplacian energy, and Signless Laplacian energy. Keywords: Laplacian Energy, Spectrum, Seidel Matrix, Signless Laplacian Matrix, Edge Antimagic Graphs.
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7

M, Simaringa, and Santhoshkumar K. "Prime Graphs of Some Graphs." Journal of Advanced Research in Dynamical and Control Systems 12, no. 8 (August 19, 2020): 51–55. http://dx.doi.org/10.5373/jardcs/v12i8/20202445.

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8

Zhang, Xiaoling, and Chengyuan Song. "The Distance Matrices of Some Graphs Related to Wheel Graphs." Journal of Applied Mathematics 2013 (2013): 1–5. http://dx.doi.org/10.1155/2013/707954.

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LetDdenote the distance matrix of a connected graphG. The inertia ofDis the triple of integers (n+(D), n0(D), n-(D)), wheren+(D),n0(D), andn-(D)denote the number of positive, 0, and negative eigenvalues ofD, respectively. In this paper, we mainly study the inertia of distance matrices of some graphs related to wheel graphs and give a construction for graphs whose distance matrices have exactly one positive eigenvalue.
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9

Rashed, Payman A. "The Nullity of Identifying Path Graph with Some Special Graphs." Journal of Zankoy Sulaimani - Part A 19, no. 2 (November 20, 2016): 185–94. http://dx.doi.org/10.17656/jzs.10622.

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10

Zelinka, Bohdan. "Small directed graphs as neighbourhood graphs." Czechoslovak Mathematical Journal 38, no. 2 (1988): 269–73. http://dx.doi.org/10.21136/cmj.1988.102221.

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11

Knor, Martin, and Ľudovít Niepel. "Graphs isomorphic to their path graphs." Mathematica Bohemica 127, no. 3 (2002): 473–80. http://dx.doi.org/10.21136/mb.2002.134066.

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12

PERARNAU, G., and B. REED. "Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree." Combinatorics, Probability and Computing 26, no. 3 (December 7, 2016): 448–67. http://dx.doi.org/10.1017/s0963548316000328.

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Let ℱ be a family of graphs and letdbe large enough. For everyd-regular graphG, we study the existence of a spanning ℱ-free subgraph ofGwith large minimum degree. This problem is well understood if ℱ does not contain bipartite graphs. Here we provide asymptotically tight results for many families of bipartite graphs such as cycles or complete bipartite graphs. To prove these results, we study a locally injective analogue of the question.
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13

Chartrand, Gary, Donald W. Vanderjagt, and Ping Zhang. "Homogeneously embedding stratified graphs in stratified graphs." Mathematica Bohemica 130, no. 1 (2005): 35–48. http://dx.doi.org/10.21136/mb.2005.134221.

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14

Weiss, Scott. "Graphs on Graphs." ACM Inroads 14, no. 1 (February 21, 2023): 56. http://dx.doi.org/10.1145/3583107.

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15

Srinivasan, Sakunthala, and Vimala Shanmugavel. "Minimum Degree Energy of Graphs and Pebbling Graphs." Indian Journal Of Science And Technology 17, no. 18 (April 24, 2024): 1838–44. http://dx.doi.org/10.17485/ijst/v17i18.778.

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Objectives: The minimum degree energy concept is applied to pebbling graphs. This study establishes a connection between the minimum degree energy of graphs and the minimum degree energy of pebbling graphs by applying the lowest degree energy of pebbling notion to twenty standard graphs. Methods: The minimum degree energy of pebbling graph with the matrix whose was calculated using . The characteristic polynomial of the minimum degree, is must be found from the matrix. Next, the eigen values of the matrix were calculated using and the sum of all the eigen values gives the minimum degree energy. The lower and upper bounds for the minimum degree energy of graphs are established along with the algorithm for computing the minimum degree energy of graphs. Findings: The lower and upper bounds were found for the minimum degree energy of pebbling graphs. For twenty standard graphs and pebbling graphs, the minimum degree energy values were calculated, and their relation was tabulated. Novelty: Pebbling graphs were subjected to the minimal energy idea and a relationship was found between the minimum energy of pebbling graphs and the minimum energy of graphs in general. Keywords: Energy, Minimum degree energy, Grotzsch graph, Pebbling graph, Data mining
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16

Khorsandi, Mahdi Reza. "Graphs whose line graphs are ring graphs." AKCE International Journal of Graphs and Combinatorics 17, no. 3 (July 2, 2020): 801–3. http://dx.doi.org/10.1016/j.akcej.2019.10.002.

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17

Manthiram, Bramila, and Meenakshi Annamalai. "Some Standard Seidel Energy Results of the Minimum Maximal Dominating Graphs." Indian Journal Of Science And Technology 17, no. 12 (March 20, 2024): 1231–36. http://dx.doi.org/10.17485/ijst/v17i12.52.

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Objectives: Let be a finite and connected graph with β points and d edges. In this research, introduced the graph's minimum maximal dominating seidel energy ( and the properties of the latent roots of the given parameters are discussed. Method: In this research, the seidel energy of several graphs and its properties are investigated. Examined its minimum maximal limits and computed a few conventional seidel energy outcomes for the minimum maximal dominating graphs. Finding: Using the minimum maximal dominating seidel energy of graphs, significant outcomes were achieved for complete graphs, complete bipartite graphs, and star graphs. The properties of the class of graphs were computed. The established upper and lower bound is . Novelty: The seidel energy of the proposed research findings is used in various graphs based on the research. The fundamental characteristics of a graph, such as its energy upper and lower bounds, have been determined, and this knowledge has found notable chemical applications in the conjugated molecular orbital theory. Recommendations for future energy-related research are presented and examined. Keywords: Connected graph, Dominating set, Latent roots, Minimum maximal, Seidel energy
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18

Basavanagoud, B., and Veena Mathad. "Graph Equations for Line Graphs, Jump Graphs, Middle Graphs, Splitting Graphs And Line Splitting Graphs." Mapana - Journal of Sciences 9, no. 2 (November 30, 2010): 53–61. http://dx.doi.org/10.12723/mjs.17.7.

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For a graph G, let G, L(G), J(G) S(G), L,(G) and M(G) denote Complement, Line graph, Jump graph, Splitting graph, Line splitting graph and Middle graph respectively. In this paper, we solve the graph equations L(G) =S(H), M(G) = S(H), L(G) = LS(H), M(G) =LS(H), J(G) = S(H), M(G) = S(H), J(G) = LS(H) and M(G) = LS(G). The equality symbol '=' stands for on isomorphism between two graphs.
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19

Nishanthini, Radhakrishnan, Ramasamy Jeyabalan, Samipillai Balasundar, and Gurunathan Kumar. "Consecutive z-index vertex magic labeling graphs." Journal of Intelligent & Fuzzy Systems 41, no. 1 (August 11, 2021): 219–30. http://dx.doi.org/10.3233/jifs-201489.

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The conception of magic labeling in fuzzy graphs elongates to fuzzy vertex magic labeling together with consecutive non-integer values in (0, 1] and the graph’s repercussion is named as fuzzy consecutive vertex magic labeling graphs (FCVM) along with the z-index. In this manuscript, we give some properties associated with FCVM labeling along with z-index as well as the presence of FCVM labeling with z-index in trees and some generalizations. Moreover, we examine the FCVM labeling along with z-index of both regular and irregular graphs. Finally, in real-time applications, we bestow an instance for fuzzy consecutive vertex magic labeling graphs.
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20

Holleis, Paul, Thomas Zimmermann, and Daniel Gmach. "Drawing Graphs Within Graphs." Journal of Graph Algorithms and Applications 9, no. 1 (2005): 7–18. http://dx.doi.org/10.7155/jgaa.00097.

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21

Fricke, Gerd H., Sandra M. Hedetniemi, Stephen T. Hedetniemi, and Kevin R. Hutson. "γ-graphs of graphs." Discussiones Mathematicae Graph Theory 31, no. 3 (2011): 517. http://dx.doi.org/10.7151/dmgt.1562.

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22

Alsardary, Salar Y. "A note on small directed graphs as neighborhood graphs." Czechoslovak Mathematical Journal 44, no. 4 (1994): 577–78. http://dx.doi.org/10.21136/cmj.1994.128492.

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23

You, Lihua, Jieshan Yang, Yingxue Zhu, and Zhifu You. "The Maximal Total Irregularity of Bicyclic Graphs." Journal of Applied Mathematics 2014 (2014): 1–9. http://dx.doi.org/10.1155/2014/785084.

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In 2012, Abdo and Dimitrov defined the total irregularity of a graphG=(V,E)asirrtG=1/2∑u,v∈VdGu-dGv, wheredGudenotes the vertex degree of a vertexu∈V. In this paper, we investigate the total irregularity of bicyclic graphs and characterize the graph with the maximal total irregularity among all bicyclic graphs onnvertices.
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24

Gao, Wei, Muhammad Kamran Jamil, Aisha Javed, Mohammad Reza Farahani, Shaohui Wang, and Jia-Bao Liu. "Sharp Bounds of the Hyper-Zagreb Index on Acyclic, Unicylic, and Bicyclic Graphs." Discrete Dynamics in Nature and Society 2017 (2017): 1–5. http://dx.doi.org/10.1155/2017/6079450.

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The hyper-Zagreb index is an important branch in the Zagreb indices family, which is defined as∑uv∈E(G)‍(d(u)+d(v))2, whered(v)is the degree of the vertexvin a graphG=(V(G),E(G)). In this paper, the monotonicity of the hyper-Zagreb index under some graph transformations was studied. Using these nice mathematical properties, the extremal graphs amongn-vertex trees (acyclic), unicyclic, and bicyclic graphs are determined for hyper-Zagreb index. Furthermore, the sharp upper and lower bounds on the hyper-Zagreb index of these graphs are provided.
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25

Kaliszewski, S., Alex Kumjian, John Quigg, and Aidan Sims. "Topological realizations and fundamental groups of higher-rank graphs." Proceedings of the Edinburgh Mathematical Society 59, no. 1 (June 10, 2015): 143–68. http://dx.doi.org/10.1017/s0013091515000061.

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AbstractWe investigate topological realizations of higher-rank graphs. We show that the fundamental group of a higher-rank graph coincides with the fundamental group of its topological realization. We also show that topological realization of higher-rank graphs is a functor and that for each higher-rank graphΛ, this functor determines a category equivalence between the category of coverings ofΛand the category of coverings of its topological realization. We discuss how topological realization relates to two standard constructions fork-graphs: projective limits and crossed products by finitely generated free abelian groups.
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26

O’Keeffe, Michael, and Michael M. J. Treacy. "Embeddings of Graphs: Tessellate and Decussate Structures." International Journal of Topology 1, no. 1 (March 29, 2024): 1–10. http://dx.doi.org/10.3390/ijt1010001.

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We address the problem of finding a unique graph embedding that best describes a graph’s “topology” i.e., a canonical embedding (spatial graph). This question is of particular interest in the chemistry of materials. Graphs that admit a tiling in 3-dimensional Euclidean space are termed tessellate, those that do not decussate. We give examples of decussate and tessellate graphs that are finite and 3-periodic. We conjecture that a graph has at most one tessellate embedding. We give reasons for considering this the default “topology” of periodic graphs.
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27

Radha, K., and A. Jasmine Kingsly. "Cardinality and Isomorphic Properties of Hajós Graphs and Hajós Fuzzy Graphs." Indian Journal Of Science And Technology 17, no. 37 (October 5, 2024): 3871–80. http://dx.doi.org/10.17485/ijst/v17i37.2492.

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Objectives: Fuzzy graphs allow uncertainty in the ideas characterizing vertices and edges to be included when modelling real-world scenarios into graph models. This study aims to introduce Hajós fuzzy graph, cardinality of Hajós graph and Hajós fuzzy graph and to explore many properties. Methods : Here, the Hajós construction is applied to two fuzzy graphs, and the Hajós fuzzy graph is defined by assigning membership values to all the edges and vertices of the newly formed fuzzy graph. Fuzzy graph conditions are verified for the assigned membership values. Examples are used to illustrate the concept. Findings: The Hajós fuzzy graph's size and order are established. Isomorphic property is discussed. The number of Hajós (fuzzy) graphs that exist for some combinations of two (fuzzy) graphs is calculated. Novelty: Based on Hajós construction, the Hajós fuzzy graph is defined. Based on the fact that different choices of vertices and edges produce different Hajós (fuzzy) graph, its cardinality is defined. The notion of cardinality is a novel concept in Hajos graph which helps to find the total number of Hajós (fuzzy) graphs. The cardinality of the Hajós (fuzzy) graph which arises from two (fuzzy) graphs that can be a cycle, path, regular graph, complete graph and complete bipartite graph are derived. Mathematics subject classification. (2010): 05C72, 05C76 Keywords: Hajós Graph, Hajós fuzzy graph, Order, Size, Isomorphism, Cardinality of Hajós fuzzy graph
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28

M, Jerlin Seles, and Dr U. Mary. "Strategy on Disaster Recovery Management based on Graph Theory Concepts." International Journal of Recent Technology and Engineering (IJRTE) 10, no. 4 (November 30, 2021): 31–34. http://dx.doi.org/10.35940/ijrte.d6535.1110421.

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The COVID-19 pandemic has asserted major baseline facts from disaster anthropology during the last three decades. Resilience could be based on the solution to the question: "What is the maximum amount of destruction, if any, that the graph (a network) can sustain while ensuring that at least one of each technology type remains and that the remaining induced subgraph is properly colored?" The concept of a graph's Chromatic Core Subgraph is a solution to the stated problem. In this paper, the pandemic graphs and certain sequential graphs are developed. For these graphs, the Chromatic core subgraph is obtained. The results of the pandemic graphs' Chromatic core subgraph are used to develop a disaster recovery strategy for the COVID-19 pandemic.
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29

Eshghi, Kourosh. "Extension ofα-labelings of quadratic graphs." International Journal of Mathematics and Mathematical Sciences 2004, no. 11 (2004): 571–78. http://dx.doi.org/10.1155/s0161171204306010.

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First, a new proof for the existence of anα-labeling of the quadratic graphQ(3,4k)is presented. Then the existence ofα-labelings of special classes of quadratic graphs with some isomorphic components is shown.
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30

Praveenkumar, L., G. Mahadevan, and C. Sivagnanam. "Generalization of CD-Number for Power Graph of Some Special Types of Tree Graphs." Indian Journal Of Science And Technology 17, SPI1 (April 25, 2024): 109–14. http://dx.doi.org/10.17485/ijst/v17sp1.223.

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Objectives: The main objective of the article is to finding the corona domination for the power graph of some special types of tree graph. Method: A dominating set of a graph is said to be a corona dominating set if every vertex in is either a pendant vertex or a support vertex. The minimum cardinality of a corona dominating set is called the corona domination number and is denoted by . Findings: In this article, we study the -number for the power of PVB-tree and where and identify their exact values. Novelty: The corona domination was one of the recently developed domination parameter, along with this parameter we found the exact value for some special types of graphs. Keywords: Domination Number, Corona Domination Number, Total Domination, Power Graphs, Olive Tree And PVB­Tree
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31

Groshaus, Marina, and André L. P. Guedes. "Biclique Graphs of K3-free Graphs and Bipartite Graphs." Procedia Computer Science 195 (2021): 230–38. http://dx.doi.org/10.1016/j.procs.2021.11.029.

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32

Le, Van Bang. "On opposition graphs, coalition graphs, and bipartite permutation graphs." Discrete Applied Mathematics 168 (May 2014): 26–33. http://dx.doi.org/10.1016/j.dam.2012.11.020.

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33

Cherlin, Gregory. "Henson graphs and Urysohn—Henson graphs as Cayley graphs." Functional Analysis and Its Applications 49, no. 3 (July 2015): 189–200. http://dx.doi.org/10.1007/s10688-015-0103-2.

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34

Liu, Yu, and Lihua You. "Further Results on the Nullity of Signed Graphs." Journal of Applied Mathematics 2014 (2014): 1–8. http://dx.doi.org/10.1155/2014/483735.

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The nullity of a graph is the multiplicity of the eigenvalue zero in its spectrum. A signed graph is a graph with a sign attached to each of its edges. In this paper, we apply the coefficient theorem on the characteristic polynomial of a signed graph and give two formulae on the nullity of signed graphs with cut-points. As applications of the above results, we investigate the nullity of the bicyclic signed graphΓ∞p,q,l, obtain the nullity set of unbalanced bicyclic signed graphs, and thus determine the nullity set of bicyclic signed graphs.
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35

Nebeský, Ladislav. "The interval function of a connected graph and a characterization of geodetic graphs." Mathematica Bohemica 126, no. 1 (2001): 247–54. http://dx.doi.org/10.21136/mb.2001.133909.

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36

Sebastian, Reena, and K. A. Germina K.A Germina. "On Square Sum Chain Graphs whose Blocks are Complete Graphs." International Journal of Scientific Research 3, no. 2 (June 1, 2012): 298–304. http://dx.doi.org/10.15373/22778179/feb2014/95.

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37

Chaplick, Steven, and Torsten Ueckerdt. "Planar Graphs as VPG-Graphs." Journal of Graph Algorithms and Applications 17, no. 4 (2013): 475–94. http://dx.doi.org/10.7155/jgaa.00300.

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38

Bergstrand, Deborah, Ken Hodges, George Jennings, Lisa Kuklinski, Janet Wiener, and Frank Harary. "Product Graphs Are Sum Graphs." Mathematics Magazine 65, no. 4 (October 1, 1992): 262. http://dx.doi.org/10.2307/2691455.

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39

Palani, K., T. Jones, and V. Maheswari. "Soft Graphs of Certain Graphs." Journal of Physics: Conference Series 1947, no. 1 (June 1, 2021): 012045. http://dx.doi.org/10.1088/1742-6596/1947/1/012045.

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40

DAMIAN, MIRELA, and KRISTIN RAUDONIS. "YAO GRAPHS SPAN THETA GRAPHS." Discrete Mathematics, Algorithms and Applications 04, no. 02 (June 2012): 1250024. http://dx.doi.org/10.1142/s1793830912500243.

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Yao and Theta graphs are defined for a given point set and a fixed integer k > 0. The space around each point is divided into k cones of equal angle, and each point is connected to a nearest neighbor in each cone. The difference between Yao and Theta graphs is in the way the nearest neighbor is defined: Yao graphs minimize the Euclidean distance between a point and its neighbor, and Theta graphs minimize the Euclidean distance between a point and the orthogonal projection of its neighbor on the bisector of the hosting cone. We prove that, corresponding to each edge of the Theta graph Θ6, there is a path in the Yao graph Y6 whose length is at most 8.82 times the edge length. Combined with the result of Bonichon et al., who prove an upper bound of 2 on the stretch factor of Θ6, we obtain an upper bound of 17.64 on the stretch factor of Y6.
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41

Cvetkovic, Dragos, and Vesna Todorcevic. "Cospectrality graphs of Smith graphs." Filomat 33, no. 11 (2019): 3269–76. http://dx.doi.org/10.2298/fil1911269c.

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Graphs whose spectrum belongs to the interval [-2,2] are called Smith graphs. The structure of a Smith graph with a given spectrum depends on a system of Diophantine linear algebraic equations. We have established in [1] several properties of this system and showed how it can be simplified and effectively applied. In this way a spectral theory of Smith graphs has been outlined. In the present paper we introduce cospectrality graphs for Smith graphs and study their properties through examples and theoretical consideration. The new notion is used in proving theorems on cospectrality of Smith graphs. In this way one can avoid the use of the mentioned system of Diophantine linear algebraic equations.
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42

Bergstrand, Deborah, Ken Hodges, George Jennings, Lisa Kuklinski, Janet Wiener, and Frank Harary. "Product Graphs are Sum Graphs." Mathematics Magazine 65, no. 4 (October 1992): 262–64. http://dx.doi.org/10.1080/0025570x.1992.11996034.

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43

Hajnal, A., and P. Komj{áth. "Embedding graphs into colored graphs." Transactions of the American Mathematical Society 307, no. 1 (January 1, 1988): 395. http://dx.doi.org/10.1090/s0002-9947-1988-0936824-0.

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Sato, Iwao. "Clique graphs of packed graphs." Discrete Mathematics 62, no. 1 (October 1986): 107–9. http://dx.doi.org/10.1016/0012-365x(86)90048-8.

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Pretzel, Oliver, and Dale Youngs. "Balanced graphs and noncovering graphs." Discrete Mathematics 88, no. 2-3 (April 1991): 279–87. http://dx.doi.org/10.1016/0012-365x(91)90015-t.

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Fox, Jacob, and János Pach. "String graphs and incomparability graphs." Advances in Mathematics 230, no. 3 (June 2012): 1381–401. http://dx.doi.org/10.1016/j.aim.2012.03.011.

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Dale, M. R. T., and M. J. Fortin. "From Graphs to Spatial Graphs." Annual Review of Ecology, Evolution, and Systematics 41, no. 1 (December 2010): 21–38. http://dx.doi.org/10.1146/annurev-ecolsys-102209-144718.

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Thirusangu, K., and K. Rangarajan. "Marked graphs and Euler graphs." Microelectronics Reliability 37, no. 2 (February 1997): 225–35. http://dx.doi.org/10.1016/s0026-2714(96)00111-4.

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Thirusangu, K., and K. Rangarajan. "Marked graphs and hamiltonian graphs." Microelectronics Reliability 37, no. 8 (August 1997): 1243–50. http://dx.doi.org/10.1016/s0026-2714(97)00001-2.

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Zhou, Sanming. "Symmetric Graphs and Flag Graphs." Monatshefte f�r Mathematik 139, no. 1 (April 1, 2003): 69–81. http://dx.doi.org/10.1007/s00605-002-0538-4.

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