Results 21 to 30 of about 3,100,536 (300)
An upper bound for difference of energies of a graph and its complement
Examples and Counterexamples, 2023 The A-energy of a graph G, denoted by EA(G), is defined as sum of the absolute values of eigenvalues of adjacency matrix of G. Nikiforov in Nikiforov (2016) proved that EA(G¯)−EA(G)≤2μ¯1and EA(G)−EA(G¯)≤2μ1for any graph G and posed a problem to find best
Harishchandra S. Ramane +2 more
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Extension of Strongly Regular Graphs [PDF]
The Electronic Journal of Combinatorics, 2008 The Friendship Theorem states that if any two people in a party have exactly one common friend, then there exists a politician who is a friend of everybody. In this paper, we generalize the Friendship Theorem. Let $\lambda$ be any nonnegative integer and $\mu$ be any positive integer.
Gera, Ralucca, Shen, J.
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On the Integrability of Strongly Regular Graphs [PDF]
Graphs and Combinatorics, 2019 Koolen et al. showed that if a connected graph with smallest eigenvalue at least $-3$ has large minimal valency, then it is $2$-integrable. In this paper, we will prove that a lower bound for the minimal valency is 166.
Jack H. Koolen +2 more
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Examples and Counterexamples, 2023 A new strongly regular graph with parameters (81,30,9,12) is found as a graph invariant under certain subgroup of the full automorphism group of the previously known strongly regular graph discovered in 1981 by J. H. van Lint and A. Schrijver.
Dean Crnković, Andrea Švob
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DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {27, 20, 7; 1, 4, 21} DOES NOT EXIST
Ural Mathematical Journal, 2020 In the class of distance-regular graphs of diameter 3 there are 5 intersection arrays of graphs with at most 28 vertices and noninteger eigenvalue. These arrays are \(\{18,14,5;1,2,14\}\), \(\{18,15,9;1,1,10\}\), \(\{21,16,10;1,2,12\}\), \(\{24,21,3;1,3 ...
Konstantin S. Efimov +1 more
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MASALAH EIGEN DAN EIGENMODE MATRIKS ATAS ALJABAR MIN-PLUS
Barekeng, 2021 Eigen problems and eigenmode are important components related to square matrices. In max-plus algebra, a square matrix can be represented in the form of a graph called a communication graph.
Eka Widia Rahayu +2 more
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A unique and novel graph matrix for efficient extraction of structural information of networks
Electronic Journal of Graph Theory and Applications, 2021 In this article, we propose a new type of square matrix associated with an undirected graph by trading off the natural embedded symmetry in them. The proposed matrix is defined using the neighbourhood sets of the vertices, called as neighbourhood matrix
Sivakumar Karunakaran +1 more
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Cyclotomy and Strongly Regular Graphs [PDF]
Journal of Algebraic Combinatorics, 1999 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Brouwer, A. E. +2 more
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AUTOMORPHISMS OF DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {39; 36; 4; 1; 1; 36}
Ural Mathematical Journal, 2018 Makhnev and Nirova have found intersection arrays of distance-regular graphs with no more than \(4096\) vertices, in which \(\lambda=2\) and \(\mu=1\). They proposed the program of investigation of distance-regular graphs with \(\lambda=2\) and \(\mu=1\)
Konstantin S. Efimov +1 more
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AUTOMORPHISMS OF DISTANCE-REGULAR GRAPH WITH INTERSECTION ARRAY {25; 16; 1; 1; 8; 25}
Ural Mathematical Journal, 2017 Makhnev and Samoilenko have found parameters of strongly regular graphs with no more than 1000 vertices, which may be neighborhoods of vertices in antipodal distance-regular graph of diameter 3 and with \(\lambda=\mu\).
Konstantin S. Efimov +1 more
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