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Cubic vertex-transitive graphs of order 2pq

✍ Scribed by Jin-Xin Zhou; Yan-Quan Feng

Publisher: John Wiley and Sons
Year: 2010
Tongue: English
Weight: 166 KB
Volume: 65
Category: Article
ISSN: 0364-9024
DOI: 10.1002/jgt.20481

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✦ Synopsis

A graph is vertex-transitive or symmetric if its automorphism group acts transitively on vertices or ordered adjacent pairs of vertices of the graph, respectively. Let G be a finite group and S a subset of G such that 1 / ∈ S and S = {s -1 | s ∈ S}. The Cayley graph Cay(G, S) on G with respect to S is defined as the graph with vertex set G and edge set {{g, sg} | g ∈ G, s ∈ S}. Feng and Kwak [J Combin Theory B 97 (2007), 627-646; J Austral Math Soc 81 (2006), 153-164] classified all cubic symmetric graphs of order 4p or 2p 2 and in this article we classify all cubic symmetric graphs of order 2pq, where p and q are distinct odd primes. Furthermore, a classification of all cubic vertex-transitive non-Cayley graphs of order 2pq, which were investigated extensively in the literature, is given. As a result, among others, a classification of cubic vertex-transitive graphs of order 2pq can be deduced.

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