On Isomorphisms of Vertex-transitive Graphs

2016/02/24 by Jing Chen, Chen, Jing, Binzhou Xia +1
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #math.CO #math.GR

paper · pdf · doi:10.48550/arxiv.1602.07501

arxiv created 2016/03/27 · arxiv updated 2016/03/29

Abstract

The isomorphism problem of Cayley graphs has been well studied in the literature, such as characterizations of CI (DCI)-graphs and CI (DCI)-groups. In this paper, we generalize these to vertex-transitive graphs and establish parallel results. Some interesting vertex-transitive graphs are given, including a first example of connected symmetric non-Cayley non-GI-graph. Also, we initiate the study for GI and DGI-groups, defined analogously to the concept of CI and DCI-groups.

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