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1

Potgieter, Zelda. "Lacan’s three orders, the graphe complet and music in film:." Communicare: Journal for Communication Studies in Africa 26, no. 1 (2022): 1–26. http://dx.doi.org/10.36615/jcsa.v26i1.1708.

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This article engages with the Lacanian tradition of film theory in order to suggest some of the waysin which music in film may be understood to contribute significantly to subject identification in filmicexperience. Two points are argued: 1) that Lacan’s distinction between the three orders - the Real,the Imaginary and the Symbolic - may usefully be understood in musical terms, and, 2) that thetwo vectors of Lacan’s graphe complet – the vector of speech and the vector of drive – providemeaningful insight into the manner in which the three orders shape filmic musical experience.Analysis of Mikl
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2

Wafiq, Hibi. "Non-Isomorphism Between Graph And Its Complement." Multicultural Education 7, no. 6 (2021): 256. https://doi.org/10.5281/zenodo.4965942.

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<em>It is known that any graph with six vertices cannot be isomorphic to its complement [3].V. K. Balakrishnan has written in his book Schaum&rsquo;s solved problems series [1] the following: &ldquo;Given two arbitrary Simple graphs of the same order and the same size, the problem of determining whetheran isomorphism exists between the two is known as the isomorphism problem in graph theory. In general, itis not all easy (in other words, there is no &quot;efficient algorithm&quot;) to solve an arbitrary instance of the isomorphismproblem&rdquo;, from here came the idea of this paper. As mentio
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3

S., Sylvia Vergara. "Complete graph immersions in dense graphs." Discrete Mathematics 340, no. 5 (2017): 1019–27. http://dx.doi.org/10.1016/j.disc.2017.01.001.

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4

Harris, Haylee Aileen. "The Coloring Graph of Complete Graphs." PUMP Journal of Undergraduate Research 2 (September 6, 2019): 150–60. http://dx.doi.org/10.46787/pump.v2i0.1448.

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We study the coloring graph of the family of complete graphs and we prove that Cn(Kt) is regular, transitive, and connected when n&gt;t. Also, we study whether Cn(Kt) is distance transitive or strongly regular, and find its diameter.
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5

Wang, Jinhua, and Dengju Ma. "Petersen Graph Decompositions of Complete Multipartite Graphs." Graphs and Combinatorics 26, no. 5 (2010): 737–44. http://dx.doi.org/10.1007/s00373-010-0925-x.

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6

Erdős, P., and L. Pyber. "Covering a graph by complete bipartite graphs." Discrete Mathematics 170, no. 1-3 (1997): 249–51. http://dx.doi.org/10.1016/s0012-365x(96)00124-0.

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7

A, Punitha Tharani, and Saradha P. "Discrete Labeling of Graphs." Indian Journal of Science and Technology 17, SP1 (2024): 93–102. https://doi.org/10.17485/IJST/v17sp1.176.

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Abstract <strong>Objectives:</strong>&nbsp;To introduce a new type of labeling called Discrete Labeling. This labeling aims at providing the maximum output whenever the inputs are distinct with rational distribution of neighbours thereby exhibiting the stronger form of Cordial labeling. This work serves as an aid in decision-making.<strong>&nbsp;Methods:</strong>&nbsp;The discrete labels 0 and 1 are cordially assigned to the vertices such that the edges receive labels depending on the incident vertex labels using EX-OR operation with the condition that for every vertex the cardinality of neigh
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8

Shelah, Saharon. "Universality among graphs omitting a complete bipartite graph." Combinatorica 32, no. 3 (2012): 325–62. http://dx.doi.org/10.1007/s00493-012-2033-4.

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9

Vijayalakshmi, S., S. Geetha, and S. Sahaya Arockia Selvi. "Complete Intuitionistic Fuzzy Graphs." International Journal of Science and Research (IJSR) 11, no. 11 (2022): 1021–26. http://dx.doi.org/10.21275/sr221107184909.

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10

Abdul Razak, M. N. S., W. H. Fong, and N. H. Sarmin. "Graph splicing rules with cycle graph and its complement on complete graphs." Journal of Physics: Conference Series 1988, no. 1 (2021): 012067. http://dx.doi.org/10.1088/1742-6596/1988/1/012067.

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11

Garciano, A. D., M. C. T. Lagura, and R. M. Marcelo. "Sigma chromatic number of graph coronas involving complete graphs." Journal of Physics: Conference Series 1538 (May 2020): 012003. http://dx.doi.org/10.1088/1742-6596/1538/1/012003.

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12

Olesky, D. D., P. van den Driessche, and J. H. Verner. "Graphs with the same determinant as a complete graph." Linear Algebra and its Applications 312, no. 1-3 (2000): 191–95. http://dx.doi.org/10.1016/s0024-3795(00)00114-2.

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13

Keil, J. Mark, and Carl A. Gutwin. "Classes of graphs which approximate the complete euclidean graph." Discrete & Computational Geometry 7, no. 1 (1992): 13–28. http://dx.doi.org/10.1007/bf02187821.

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14

Wang, Hong. "Packing two bipartite graphs into a complete bipartite graph." Journal of Graph Theory 26, no. 2 (1997): 95–104. http://dx.doi.org/10.1002/(sici)1097-0118(199710)26:2<95::aid-jgt4>3.0.co;2-a.

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15

Murugan, A. Nellai, and G. Victor Emmanuel. "Complete Dominating Number of Graphs." Indian Journal of Applied Research 4, no. 1 (2011): 348–50. http://dx.doi.org/10.15373/2249555x/jan2014/102.

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16

Aslam, Adnan, Juan Luis Garc´ıa Guirao, Safyan Ahmad, and Wei Gao. "Topological Indices of the Line Graph of Subdivision Graph of Complete Bipartite Graphs." Applied Mathematics & Information Sciences 11, no. 6 (2017): 1631–36. http://dx.doi.org/10.18576/amis/110610.

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17

PERARNAU, G., та B. REED. "Existence of Spanning ℱ-Free Subgraphs with Large Minimum Degree". Combinatorics, Probability and Computing 26, № 3 (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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18

Wu, Keshou, Guanfeng Liu, and Junwen Lu. "Graph-Based Node Finding in Big Complex Contextual Social Graphs." Complexity 2020 (February 26, 2020): 1–13. http://dx.doi.org/10.1155/2020/7909826.

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Graph pattern matching is to find the subgraphs matching the given pattern graphs. In complex contextual social networks, considering the constraints of social contexts like the social relationships, the social trust, and the social positions, users are interested in the top-K matches of a specific node (denoted as the designated node) based on a pattern graph, rather than the entire set of graph matching. This inspires the conText-Aware Graph pattern-based top-K designated node matching (TAG-K) problem, which is NP-complete. Targeting this challenging problem, we propose a recurrent neural ne
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19

Ismayil, A. Mohamed, and N. Azhagendran. "Isomorphism on Complex Fuzzy Graph." Indian Journal Of Science And Technology 17, SPI1 (2024): 86–92. http://dx.doi.org/10.17485/ijst/v17sp1.165.

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Objective: To investigate isomorphism between two complex fuzzy graphs and prove it is an equivalence relation. The major objective of this research paper is to elucidate weak and strong isomorphism, and the study also endeavours to look at the complement of complex fuzzy graphs. Methods: Isomorphism is examined by comparing the membership values of nodes and arcs (both amplitude and phase). The same technique also proves further validation of the equivalence relation, which is also proven by the same technique. This criterion helps us to identify and formalise the isomorphic relationship betw
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20

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 (2012): 298–304. http://dx.doi.org/10.15373/22778179/feb2014/95.

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21

D, Vijayalakshmi. "B-CHROMATIC NUMBER OF CENTRAL GRAPH OF LADDER GRAPH AND COMPLETE GRAPH." Kongunadu Research Journal 1, no. 1 (2014): 27–28. http://dx.doi.org/10.26524/krj309.

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22

T. Selvaraj. "Connected Graph with Bacterial Graphs and Network Distance." Communications on Applied Nonlinear Analysis 31, no. 4s (2024): 113–24. http://dx.doi.org/10.52783/cana.v31.830.

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Network theory is going to analyse the set of techniques. But in a complex system network in a network of complex it has techniques to analyse the structure in a system of interacting agents. The graph theoretic representation means the system is made to apply network. The problem may be converted into graph by two components namely nodes and edges nodes are called as entities and interactions between edges are called as edges.
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23

Antonov, A. I., and V. A. Bondarenko. "Polyhedral Graphs of GRAPH PARTITIONING and COMPLETE BIPARTITE SUBGRAPH Problems." Modeling and Analysis of Information Systems 19, no. 6 (2015): 101–6. http://dx.doi.org/10.18255/1818-1015-2012-6-101-106.

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We provide an effective description of graphs of polyhedra for GRAPH PARTITIONING and COMPLETE BIPARTITE SUBGRAPH problems. We establish the fact, that the clique number for each of this problems increases exponentially with the dimension of the space.
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24

Wu, Yalong, and Haizhen Ren. "Complexity of the Operation Graphs on Cycle and Complete Graph." Journal of Physics: Conference Series 2333, no. 1 (2022): 012006. http://dx.doi.org/10.1088/1742-6596/2333/1/012006.

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Abstract The number of spanning trees (or complexity) of a graph can be used to measure the reliabilities of network and circuit design. Although many NP hard problems are related to the complexity of graphs, there are explicit formulas for the complexity of some specific graph classes. This paper mainly studies the explicit expression of the complexity of graphs obtained by graph operations. Through classical graph operations, we obtain some operation graphs generated by cycle and complete graph, and get the closed formulas for the complexity in these operation graphs. Compared with Daoud’s r
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25

Zeb, Adnan, Summaya Saif, Junde Chen, Anwar Ul Haq, Zhiguo Gong, and Defu Zhang. "Complex graph convolutional network for link prediction in knowledge graphs." Expert Systems with Applications 200 (August 2022): 116796. http://dx.doi.org/10.1016/j.eswa.2022.116796.

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26

Pogliani, Lionello. "Graph-Theoretical Indices based on Simple, General and Complete Graphs." International Journal of Chemoinformatics and Chemical Engineering 1, no. 1 (2011): 12–28. http://dx.doi.org/10.4018/ijcce.2011010102.

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Valence molecular connectivity indices are based on the concept of valence delta, d v, that can be derived from general chemical graphs or chemical pseudographs. A general graph or pseudograph has multiple edges and loops and can be used to encode, through the valence delta, chemical entities. Two graph-theoretical concepts derived from chemical pseudographs are the intrinsic (I) and the electrotopological state (E) values, which are the used to define the valence delta of the pseudoconnectivity indices, ?I,S. Complete graphs encode, through a new valence delta, the core electrons of any atoms
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27

Corneil, D. G. "Families of graphs complete for the strong perfect graph Conjecture." Journal of Graph Theory 10, no. 1 (1986): 33–40. http://dx.doi.org/10.1002/jgt.3190100106.

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28

Popat, Kalpesh M., and K. R. Shigala. "On equienergetic graphs and graph energy of some standard graphs with self loops." Proyecciones (Antofagasta) 43, no. 5 (2024): 1269–81. http://dx.doi.org/10.22199/issn.0717-6279-6022.

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Let GS be the graph of order n and containing σ self-loops. The energy E(GS) of graph GS is defined as E(GS)= Σni=1|λi- σ/n|,where λ1, λ2,…, λn, be the eigenvalues of the adjacency matrix of GS. Two non-isomorphic graphs G1 and G2 of the same order are said to be equienergetic if they have same energy. The proposed research is an effort to expand the concept of equienergetic graphs from simple graphs to graphs having self-loops. In the present work, we have obtained a pair of equienergetic graphs and the energy of complete graphs as well as complete bipartite graphs with self loops.
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29

DEACONU, VALENTIN, ALEX KUMJIAN, and JOHN QUIGG. "Group actions on topological graphs." Ergodic Theory and Dynamical Systems 32, no. 5 (2011): 1527–66. http://dx.doi.org/10.1017/s014338571100040x.

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AbstractWe define the action of a locally compact groupGon a topological graphE. This action induces a natural action ofGon theC*-correspondence ℋ(E) and on the graphC*-algebraC*(E). If the action is free and proper, we prove thatC*(E)⋊rGis strongly Morita equivalent toC*(E/G) . We define the skew product of a locally compact groupGby a topological graphEvia a cocyclec:E1→G. The group acts freely and properly on this new topological graphE×cG. IfGis abelian, there is a dual action onC*(E) such that$C^*(E)\rtimes \hat {G}\cong C^*(E\times _cG)$. We also define the fundamental group and the univ
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30

M., Vasuki, and Dinesh Kumar A. "A STUDY ON DIVISOR GRAPHS." International Journal of Advanced Trends in Engineering and Technology (IJATET) 5, no. 1 (2020): 14–18. https://doi.org/10.5281/zenodo.6078911.

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We characterized this graphs G and H for were they Cartesian product G, H always a divisor graph. We show that divisor graphs. That the ways we prove that the cycle permutation graphs of the order at least eight are divisor graphs if then only if they are perfect. Some results concerning amalgamation operations about obtaining new divisor graphs from old ones are given. Analyzing set of graphs as its vertex amalgamations of complete set of graphs, we characterize those block graphs that are divisor graphs.
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31

El-Serafi, S., R. El-Shanawany, and H. Shabana. "Orthogonal double cover of Complete Bipartite Graph by disjoint union of complete bipartite graphs." Ain Shams Engineering Journal 6, no. 2 (2015): 657–60. http://dx.doi.org/10.1016/j.asej.2014.12.002.

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32

Rajarajachozhan, R., and R. Sampathkumar. "Eulerian Cycle Decomposition Conjecture for the line graph of complete graphs." AKCE International Journal of Graphs and Combinatorics 16, no. 2 (2019): 158–62. http://dx.doi.org/10.1016/j.akcej.2018.01.012.

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33

Paul Chew, L. "There are planar graphs almost as good as the complete graph." Journal of Computer and System Sciences 39, no. 2 (1989): 205–19. http://dx.doi.org/10.1016/0022-0000(89)90044-5.

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34

Xuan Hung, Xuan Hung. "Uniquely List Colorability of Complete Split Graphs." Selecciones Matemáticas 8, no. 1 (2021): 120–24. http://dx.doi.org/10.17268/sel.mat.2021.01.11.

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35

Putri, Soraya Annisa, Akbar Nugroho Confera, Syafrudin Syafrudin, and Bimastyaji Surya Ramadan. "Compost Solid-phase Microbial Fuel Cell (CSMFC) Performance using Graphene and Graphite as Electrodes." Jurnal Presipitasi : Media Komunikasi dan Pengembangan Teknik Lingkungan 17, no. 3 (2020): 324–33. http://dx.doi.org/10.14710/presipitasi.v17i3.324-333.

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Organic waste is a type of waste produced by many sector, which need to managed appropriately. During its development, composting is one of the organic waste management efforts that is often be applied, Another alternative organic waste management in the form of Microbial Fuel Cell (MFC) has emerged. Several researchers conducted studies on MFC performance which was influenced by many factors, especially the electrode which contributes to the electron transfer process. This study has a concern about energy optimization through CSMFC technology using different electrode’s material. Electrode ma
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36

Kuske, Dietrich, and Markus Lohrey. "Some natural decision problems in automatic graphs." Journal of Symbolic Logic 75, no. 2 (2010): 678–710. http://dx.doi.org/10.2178/jsl/1268917499.

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AbstractFor automatic and recursive graphs, we investigate the following problems:(A) existence of a Hamiltonian path and existence of an infinite path in a tree(B) existence of an Euler path, bounding the number of ends, and bounding the number of infinite branches in a tree(C) existence of an infinite clique and an infinite version of set coverThe complexity of these problems is determined for automatic graphs and. supplementing results from the literature, for recursive graphs. Our results show that these problems(A) are equally complex for automatic and for recursive graphs (-complete).(B)
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37

Pardo-Guerra, Sebastian, Vivek Kurien George, and Gabriel A. Silva. "On the Graph Isomorphism Completeness of Directed and Multidirected Graphs." Mathematics 13, no. 2 (2025): 228. https://doi.org/10.3390/math13020228.

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The category of directed graphs is isomorphic to a particular category whose objects are labeled undirected bipartite graphs and whose morphisms are undirected graph morphisms that respect the labeling. Based on this isomorphism, we begin by showing that the class of all directed graphs is a Graph Isomorphism Complete class. Afterwards, by extending this categorical framework to weighted prime graphs, we prove that the categories of multidirected graphs with and without self-loops are each isomorphic to a particular category of weighted prime graphs. Consequently, we prove that these classes o
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38

Eilers, Søren, Gunnar Restorff, Efren Ruiz, and Adam P. W. Sørensen. "Geometric Classification of Graph C*-algebras over Finite Graphs." Canadian Journal of Mathematics 70, no. 2 (2018): 294–353. http://dx.doi.org/10.4153/cjm-2017-016-7.

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AbstractWe address the classification problem for graph C*-algebras of finite graphs (finitely many edges and vertices), containing the class of Cuntz-Krieger algebras as a prominent special case. Contrasting earlier work, we do not assume that the graphs satisfy the standard condition (K), so that the graph C*-algebras may come with uncountably many ideals.We find that in this generality, stable isomorphism of graph C*-algebras does not coincide with the geometric notion of Cuntz move equivalence. However, adding a modest condition on the graphs, the two notions are proved to be mutually equi
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39

Fang, Xiaona, Lihua You, and Yufei Huang. "Maximal graphs with a prescribed complete bipartite graph as a star complement." AIMS Mathematics 6, no. 7 (2021): 7153–69. http://dx.doi.org/10.3934/math.2021419.

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40

Wang, Jie, Xiying Yuan, and Lele Liu. "Regular graphs with a prescribed complete multipartite graph as a star complement." Linear Algebra and its Applications 579 (October 2019): 302–19. http://dx.doi.org/10.1016/j.laa.2019.06.004.

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Liang, Zhihe. "On cyclic decompositions of the complete graph into the 2-regular graphs." Journal of Applied Mathematics and Computing 24, no. 1-2 (2007): 261–71. http://dx.doi.org/10.1007/bf02832315.

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42

Milici, Salvatore. "Coverings of a complete graph with five-vertex and five-edge graphs." Discrete Mathematics 284, no. 1-3 (2004): 225–29. http://dx.doi.org/10.1016/j.disc.2003.11.035.

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Higazy, M. "TWO-FOLD FACTORIZATION OF THE COMPLETE BIPARTITE GRAPHS BY INFINITE GRAPH CLASSES." Advances and Applications in Discrete Mathematics 18, no. 3 (2017): 385–96. http://dx.doi.org/10.17654/dm018030385.

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Kaliraj, K., H. Naresh Kumar, and J. Vernold Vivin. "On dynamic colouring of cartesian product of complete graph with some graphs." Journal of Taibah University for Science 14, no. 1 (2020): 168–71. http://dx.doi.org/10.1080/16583655.2020.1713586.

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45

R, Stella Maragatham, and Subramanian A. "Results on Grundy Chromatic Number of Join Graph of Graphs." Ars Combinatoria 157 (December 31, 2023): 65–71. http://dx.doi.org/10.61091/ars157-06.

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A Grundy k -coloring of a graph G is a proper k -coloring of vertices in G using colors { 1 , 2 , ⋯ , k } such that for any two colors x and y , x &lt; y , any vertex colored y is adjacent to some vertex colored x . The First-Fit or Grundy chromatic number (or simply Grundy number) of a graph G , denoted by Γ ( G ) , is the largest integer k , such that there exists a Grundy k -coloring for G . It can be easily seen that Γ ( G ) equals to the maximum number of colors used by the greedy (or First-Fit) coloring of G . In this paper, we obtain the Grundy chromatic number of Cartesian Product of p
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46

Zhen, Zhwiei, Yuzhou Chen, Murat Kantarcioglu, and Yulia R. Gel. "Graph of Graphs: A New Knowledge Representation Mechanism for Graph Learning (Student Abstract)." Proceedings of the AAAI Conference on Artificial Intelligence 37, no. 13 (2023): 16386–87. http://dx.doi.org/10.1609/aaai.v37i13.27053.

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Supervised graph classification is one of the most actively developing areas in machine learning (ML), with a broad range of domain applications, from social media to bioinformatics. Given a collection of graphs with categorical labels, the goal is to predict correct classes for unlabelled graphs. However, currently available ML tools view each such graph as a standalone entity and, as such, do not account for complex interdependencies among graphs. We propose a novel knowledge representation for graph learning called a {\it Graph of Graphs} (GoG). The key idea is to construct a new abstractio
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47

Malik, M. Aslam, and M. Khalid Mahmood. "On Simple Graphs Arising from Exponential Congruences." Journal of Applied Mathematics 2012 (2012): 1–10. http://dx.doi.org/10.1155/2012/292895.

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We introduce and investigate a new class of graphs arrived from exponential congruences. For each pair of positive integersaandb, letG(n)denote the graph for whichV={0,1,…,n−1}is the set of vertices and there is an edge betweenaandbif the congruenceax≡b (mod n)is solvable. Letn=p1k1p2k2⋯prkrbe the prime power factorization of an integern, wherep1&lt;p2&lt;⋯&lt;prare distinct primes. The number of nontrivial self-loops of the graphG(n)has been determined and shown to be equal to∏i=1r(ϕ(piki)+1). It is shown that the graphG(n)has2rcomponents. Further, it is proved that the componentΓpof the simp
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48

El-Shanawany, R. "On Orthogonal Double Covers of Complete Bipartite Graphs by an Infinite Certain Graph-Path and Graph-Cycle." British Journal of Mathematics & Computer Science 4, no. 16 (2014): 2320–25. http://dx.doi.org/10.9734/bjmcs/2014/10724.

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Ye, Meng, Tongsuo Wu, Qiong Liu, and Jin Guo. "Graph properties of co-maximal ideal graphs of commutative rings." Journal of Algebra and Its Applications 14, no. 03 (2014): 1550027. http://dx.doi.org/10.1142/s0219498815500279.

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In this paper, we determine the diameters of graphs [Formula: see text] and [Formula: see text] for a ring R with infinitely many maximal ideals. We also use graph blow-up to give a complete classification of rings R whose graphs [Formula: see text] are non-empty planar graphs.
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De Caen, D., and D. G. Hoffman. "Impossibility of Decomposing the Complete Graph on n Points into $n - 1$ Isomorphic Complete Bipartite Graphs." SIAM Journal on Discrete Mathematics 2, no. 1 (1989): 48–50. http://dx.doi.org/10.1137/0402005.

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