Graphs with Cayley canonical double covers

A canonical double cover B(X) of a graph X is the direct product of X and the complete graph K2 on two vertices. In order to answer the question when a canonical double cover of a given graph is a Cayley graph, in 1992 Marušič et al. introduced the concept of generalized Cayley graphs. In this paper...

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Bibliographic Details
Published inDiscrete mathematics Vol. 342; no. 9; pp. 2542 - 2548
Main Author Hujdurović, Ademir
Format Journal Article
LanguageEnglish
Published Elsevier B.V 01.09.2019
Subjects
Canonical double cover
Cayley graph
Extended generalized Cayley graph
Generalized Cayley graph
Vertex-transitive
Extended generalized Cayley graph
Vertex-transitive
Canonical double cover
Generalized Cayley graph
Cayley graph
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Summary:A canonical double cover B(X) of a graph X is the direct product of X and the complete graph K2 on two vertices. In order to answer the question when a canonical double cover of a given graph is a Cayley graph, in 1992 Marušič et al. introduced the concept of generalized Cayley graphs. In this paper this concept is generalized to a wider class of graphs, the so-called extended generalized Cayley graphs. It is proved that the canonical double cover of a connected non-bipartite graph X is a Cayley graph if and only if X is an extended generalized Cayley graph. This corrects an incorrectly stated claim in [Discrete Math. 102 (1992), 279–285].
ISSN:0012-365X
1872-681X
DOI:10.1016/j.disc.2019.05.018