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The Graphical Regular Representations of Finite Metacyclicp-Groups

✍ Scribed by Cai Heng Li; Hyo-Seob Sim

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 136 KB
Volume: 21
Category: Article
ISSN: 0195-6698
DOI: 10.1006/eujc.2000.0397

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✦ Synopsis

A Cayley graph = Cay(G, S) is called a graphical regular representation of the group G if Aut = G. One long-standing open problem about Cayley graphs is to determine which Cayley graphs are graphical regular representations of the corresponding groups. A simple necessary condition for to be a graphical regular representation of G is Aut(G, S) = 1, where Aut(G, S) = {τ ∈ Aut(G) | S τ = S}. C. Godsil in (Europ. J. Combinatorics, 4 (1983)) proposed to characterize graphical regular representations of groups G in terms of Aut(G, S); that is, for a given class of groups G, find the conditions under which Cay(G, S) is a graphical regular representation of G if and only if Aut(G, S) = 1. The main purpose of this paper is to give a complete solution to this problem for the class of metacyclic p-groups where p is a prime.

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