✦ LIBER ✦

On Isomorphisms of Connected Cayley Graphs, II

✍ Scribed by Cai Heng Li

Publisher: Elsevier Science
Year: 1998
Tongue: English
Weight: 182 KB
Volume: 74
Category: Article
ISSN: 0095-8956
DOI: 10.1006/jctb.1998.1830

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✦ Synopsis

A Cayley graph or digraph Cay(G, S) of a finite group G is called a CI-graph of G if, for any T/G, Cay(G, S)$Cay(G, T) if and only if S _ =T for some _ # Aut(G). We study the problem of determining which Cayley graphs and digraphs for a given group are CI-graphs. A finite group G is called a connected m-DCI-group (or connected m-CI-group) if all connected Cayley digraphs (or connected Cayley graphs, respectively) of G of (out)-valency at most m are CI-graphs. For a group G, let p(G) be the smallest prime divisor of |G|. It was previously shown that all finite groups G are connected ( p(G)&1)-DCI-groups and all finite groups G are connected 2( p(G)&1)-CI-groups. In this paper, for every prime p, we construct infinitely many finite groups G such that p(G)= p and G is neither a connected p-DCI-group nor a connected 2 p-CI-group, which provides solutions for several open problems in this area.

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