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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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5-chromatic strongly regular graphs [PDF]
Discrete Mathematics, 2006 zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Fiala, N.C., Haemers, W.H.
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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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On the construction and comparison of graph irregularity indices [PDF]
Kragujevac Journal of Science, 2017 Irregularity indices are generally used for quantitative characterization of topological structure of non-regular graphs. According to a widely accepted preconception, using a topological invariant (called a graph irregularity index) for that purpose ...
Réti Tamás, Tóth-Laufer Edit
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Automorphism groups of the constituent graphs of integral distance graphs
AKCE International Journal of Graphs and Combinatorics, 2023 In this paper, we consider the automorphism groups of Cayley graphs which are a basis of a complete Boolean algebra of strongly regular graphs, one of such graph is the integral distance graph [Formula: see text] The automorphism groups of the integral ...
O. Habineza, E. Mwambene
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On the structure of compact graphs [PDF]
Opuscula Mathematica, 2017 A simple graph \(G\) is called a compact graph if \(G\) contains no isolated vertices and for each pair \(x\), \(y\) of non-adjacent vertices of \(G\), there is a vertex \(z\) with \(N(x)\cup N(y)\subseteq N(z)\), where \(N(v)\) is the neighborhood of ...
Reza Nikandish, Farzad Shaveisi
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Directed Strongly Regular Cayley Graphs over Metacyclic Groups of Order 4n
Mathematics, 2019 We construct several new families of directed strongly regular Cayley graphs (DSRCGs) over the metacyclic group M 4 n = 〈 a , b | a n = b 4 = 1 , b − 1 a b = a − 1 〉 , some of which generalize those ...
Tao Cheng, Lihua Feng, Weijun Liu
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On Automorphisms of a Distance-Regular Graph with Intersection Array {125,96,1;1,48,125} [PDF]
Учёные записки Казанского университета: Серия Физико-математические науки, 2017 J. Koolen posed the problem of studying distance-regular graphs in which neighborhoods of vertices are strongly regular graphs with the second eigenvalue ≤ t for the given positive integer t.
V.V. Bitkina, A.A. Makhnev
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The Strongly Regular $(45,12,3,3)$ Graphs [PDF]
The Electronic Journal of Combinatorics, 2006 Using two backtrack algorithms based on different techniques, designed and implemented independently, we were able to determine up to isomorphism all strongly regular graphs with parameters $v=45$, $k=12$, $\lambda=\mu=3$. It turns out that there are $78$ such graphs, having automorphism groups with sizes ranging from $1$ to $51840$.
Coolsaet, K., Degraer, J., Spence, E.
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Discrete Mathematics, 1975 Translation from Discrete Math. 13, 357-381 (1975; Zbl 0311.05122).
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