Classifying vertex-transitive graphs whose order is a product of two primes

Marušič, Dragan; Scapellato, Raffaele

doi:10.1007/bf01215350

Cited by 51 publications

(35 citation statements)

References 15 publications

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“…Such is, for example, the case of vertex-transitive graphs of order a product of two primes, see [4,6,18,19,22], and the case of vertex-transitive graphs which are graph truncations, see [1]. The hard work needed to complete these classifications suggest that the even/odd question is by no means an easy one.…”

Section: ])mentioning

confidence: 99%

Odd automorphisms in vertex-transitive graphs

2016

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An automorphism of a graph is said to be even/odd if it acts on the set of vertices as an even/odd permutation. In this article we pose the problem of determining which vertex-transitive graphs admit odd automorphisms. Partial results for certain classes of vertex-transitive graphs, in particular for Cayley graphs, are given. As a consequence, a characterization of arc-transitive circulants without odd automorphisms is obtained.

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confidence: 99%

Odd automorphisms in vertex-transitive graphs

2016

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“…Turner [56] and Marušič [34] classified vertex-transitive graphs of order p and 2p, respectively. The vertex-transitive graphs of order a product of two primes were characterized in [38,39]. Based on our classifications of cubic VNC-graphs of order 2pq, together with the classification of cubic non-symmetric Cayley graphs of order 2pq [65] (the proof is not difficult, but tedious), one may deduce a classification of cubic vertex-transitive graphs of order 2pq.…”

Section: Introductionmentioning

confidence: 99%

Cubic vertex‐transitive graphs of order 2pq

Zhou

Feng

2010

Journal of Graph Theory

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Abstract: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 nonCayley 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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“…We remark that metacirculants were first introduced by Alspach and Parsons [2] in 1982, with more restricted conditions, refer to [19,31]. The class of metacirculants provides a rich source of many interesting families of graphs, and has been extensively studied, see for example [25] and [3,8,23,30,33]. In particular, the following is a long-standing open problem in algebraic graph theory.…”

Section: Introductionmentioning

confidence: 99%