Results 71 to 80 of about 18,773 (121)
Cayley digraphs with normal adjacency matrices
Discrete Mathematics, 2009 Let \(G\) be a finite group and \(S\) a subset of \(G\) which does not contain the identity element. The Cayley digraph \(D(G,S)\) is the digraph with \(G\) as vertex set and \(\{(g, sg): g\in G,\;s\in S\}\) as arc-set. The digraph \(D(G,S)\) is regular of degree the cardinality of \(S\).
David S. Lyubshin, Sergey V. Savchenko
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On automorphisms of Cayley-digraphs of abelian groups
Discrete Mathematics, 2003 Suppose \(G\) is a finite additive abelian group, then fix some subset \(B\) of \(G\), such that for the identity element \(0\) of \(G\), \(0\not\in B\). The Cayley-digraph of \(G\) with respect to \(B\) is defined as the digraph \(\Gamma(G,B)\), which has vertex set \(G\) and for any pair of elements \(x,y\) of \(G\) there is an edge from \(x\) to \(y\
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When the arc-colored line digraph of a cayley colored digraph is again a cayley colored digraph
, 1992 Let D6(G) be the Cayley colored ügraph of a finite group G generated by A. The arc-colored line digraph of a Cayley colored digraph ie obtained by appropriately coloring the arcs of its line digraph. In this paper it is shown that the group of automorphisms of D6 (G) that act as permutations on the color classes is isomorphic to the gemidirect product ...
Fiol Mora, Maria Lluïsa +2 more
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Some conclusions on Cayley digraphs and their applications to interconnection networks
, 2004 In this short communication, we survey the relationships between Cayley digraphs and their subgraphs and coset graphs with respect to subgroups and obtain some general results on homomorphism and broadcasting between them.
Wenjun Xiao, Behrooz Parhami
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digraphs/Digraphs: Digraphs 1.7.0
<p>Release for Digraphs</p ...
Markus Pfeiffer +23 more
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Endomorphisms of Cayley digraphs of rectangular groups [PDF]
, 2018 Let Cay(S,A) denote the Cayley digraph of the semigroup S with respect to the set A, where A is any subset of S. The function f : Cay(S,A) → Cay(S,A) is called an endomorphism of Cay(S,A) if for each (x, y) ∈ E(Cay(S,A)) implies (f(x), f(y)) ∈ E(Cay(S,A))
Gyurov, B. +3 more
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Large Cayley Graphs and Digraphs with Small Degree and Diameter
, 1995 We review the status of the Degree/Diameter problem for both, graphs and digraphs and present new Cayley digraphs which yield improvements over some of the previously known largest vertex transitive digraphs of given degree and ...
Hafner, P.R
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On positive and negative atoms of Cayley digraphs
Discrete Applied Mathematics, 1989 By using a counterexample, the paper disproves Hamidoune's conjecture [\textit{Y. O. Hamidoune}, Sur la séparation dans les graphes de Cayley abéliens, Discrete Math. 55, 323-326 (1985; Zbl 0567.05027)] that a Cayley digraph always contains a positive atom.
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ON CAYLEY DIGRAPHS THAT DO NOT HAVE HAMILTONIAN PATHS [PDF]
, 2013 We construct an infinite family Cay(Gi; ai, bi) of connected, 2-generated Cayley digraphs that do not have hamiltonian paths, such that the orders of the generators ai and bi are unbounded.
Dave Witte Morris
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On the non-existence of some Moore Cayley digraphs [PDF]
Anundirected Moore graph has the maximum number of vertices possible among all graphs with given maximum valency and diameter. It was shown by Bannai and Ito, and Damerell that a non-complete Moore graph must be regular of valency 2, 3, 7, or 57, where ...
Gavrilyuk, Alexander
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