Extension of strongly regular graphs.
Gera, Ralucca, Shen, Jian (2008)
The Electronic Journal of Combinatorics [electronic only]
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Gera, Ralucca, Shen, Jian (2008)
The Electronic Journal of Combinatorics [electronic only]
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Fiol, M.A. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Mohsen Ghasemi (2014)
Discussiones Mathematicae Graph Theory
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Let s be a positive integer. A graph is s-transitive if its automorphism group is transitive on s-arcs but not on (s + 1)-arcs. Let p be a prime. In this article a complete classification of tetravalent s-transitive graphs of order 3p2 is given
Wilfried Imrich, Ali Iranmanesh, Sandi Klavžar, Abolghasem Soltani (2016)
Discussiones Mathematicae Graph Theory
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In this note connected, edge-transitive lexicographic and Cartesian products are characterized. For the lexicographic product G ◦ H of a connected graph G that is not complete by a graph H, we show that it is edge-transitive if and only if G is edge-transitive and H is edgeless. If the first factor of G ∘ H is non-trivial and complete, then G ∘ H is edge-transitive if and only if H is the lexicographic product of a complete graph by an edgeless graph. This fixes an error of Li, Wang,...
Lepovic, Mirko (2011)
Serdica Mathematical Journal
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2010 Mathematics Subject Classification: 05C50. We say that a regular graph G of order n and degree r і 1 (which is not the complete graph) is strongly regular if there exist non-negative integers t and q such that |SiЗSj| = t for any two adjacent vertices i and j, and |SiЗSj| = q for any two distinct non-adjacent vertices i and j, where Sk denotes the neighborhood of the vertex k. Let l1 = r, l2 and l3 be the distinct eigenvalues of a connected strongly regular graph. Let...
Spence, E. (2000)
The Electronic Journal of Combinatorics [electronic only]
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Ashwin Ganesan (2016)
Discussiones Mathematicae Graph Theory
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Let S be a set of transpositions generating the symmetric group Sn (n ≥ 5). The transposition graph of S is defined to be the graph with vertex set {1, . . . , n}, and with vertices i and j being adjacent in T(S) whenever (i, j) ∈ S. In the present note, it is proved that two transposition graphs are isomorphic if and only if the corresponding two Cayley graphs are isomorphic. It is also proved that the transposition graph T(S) is edge-transitive if and only if the Cayley graph Cay(Sn,...
Gvozdjak, P., Širáň, J. (1994)
Acta Mathematica Universitatis Comenianae. New Series
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D. M. Cardoso, D. Cvetković (2006)
Bulletin, Classe des Sciences Mathématiques et Naturelles, Sciences mathématiques
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K. Shahul Hameed, K.A. Germina (2012)
Discussiones Mathematicae Graph Theory
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A graph whose edges are labeled either as positive or negative is called a signed graph. In this article, we extend the notion of composition of (unsigned) graphs (also called lexicographic product) to signed graphs. We employ Kronecker product of matrices to express the adjacency matrix of this product of two signed graphs and hence find its eigenvalues when the second graph under composition is net-regular. A signed graph is said to be net-regular if every vertex has constant net-degree,...
William L. Paschke (1993)
Mathematische Zeitschrift
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Pokrovskiy, A. (2011)
The Electronic Journal of Combinatorics [electronic only]
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