Normal Minimal Cayley Digraphs of Abelian Groups
نویسندگان
چکیده
منابع مشابه
NORMAL 6-VALENT CAYLEY GRAPHS OF ABELIAN GROUPS
Abstract : We call a Cayley graph Γ = Cay (G, S) normal for G, if the right regular representation R(G) of G is normal in the full automorphism group of Aut(Γ). In this paper, a classification of all non-normal Cayley graphs of finite abelian group with valency 6 was presented.
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Let S be a minimal generating subset of the finite abelian group G. We prove that if the Sylow 2-subgroup of G is cyclic, then Sand S U S-l are CI-subsets and the corresponding Cayley digraph and graph are normal. Let G be a finite group and let S be a subset of G not containing the identity element 1. The Cayley digraph X = Cay(G, S) of G with respect to S is defined by V(X) = G, E(X) = {(g,sg...
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Let Sand T be two minimal generating s~bsets of a finite abelian group G. We prove that if Cay(G, S) ~ Cay(G, T) then there exists an a E Aut(G) such that SOl = T. Let G be a finite group and S a subset of G not containing the identity element 1. The Cayley digraph X = Cay( G, S) of G with respect to S is defined by V(X) = G, E(X) = {(g,sg) I 9 E G,s E S}. It is easy to check that if a is an au...
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In the study of double-loop computer networks, the diagrams known as L-shapes arise as a graphical representation of an optimal routing for every graph’s node. The description of these diagrams provides an efficient method for computing the diameter and the average minimum distance of the corresponding graphs. We extend these diagrams to multiloop computer networks. For each Cayley digraph with...
متن کاملON THE NORMALITY OF t-CAYLEY HYPERGRAPHS OF ABELIAN GROUPS
A t-Cayley hypergraph X = t-Cay(G; S) is called normal for a finite group G, if the right regular representationR(G) of G is normal in the full automorphism group Aut(X) of X. In this paper, we investigate the normality of t-Cayley hypergraphs of abelian groups, where S < 4.
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ژورنال
عنوان ژورنال: European Journal of Combinatorics
سال: 2000
ISSN: 0195-6698
DOI: 10.1006/eujc.1999.0363