Characterizing vertex‐transitive <i>pq</i>‐graphs with an imprimitive automorphism subgroup

Marušič, Dragan; Scapellato, Raffaele

doi:10.1002/jgt.3190160410

Cited by 41 publications

(40 citation statements)

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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.…”

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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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“…For the latter, each fused-orbital graph Γ of G on Ω has order equal to a product of two primes. Such graphs Γ of G were classified in [28,29] (with two graphs associated with M 23 missed and pointed out on [22]), stated as follows. …”

Section: and Hmentioning

confidence: 99%

Finite vertex-primitive edge-transitive metacirculants

Pan

2014

J Algebr Comb

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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.…”

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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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Characterizing vertex‐transitive pq‐graphs with an imprimitive automorphism subgroup

Abstract: Vertex-transitive graphs with pq vertices, wherep and q are primes, having an imprimitive subgroup of automorphisms, are characterized. 0 1992 John Wiley & Sons, Inc.

Cited by 41 publications

References 9 publications

Odd automorphisms in vertex-transitive graphs

Odd automorphisms in vertex-transitive graphs

Finite vertex-primitive edge-transitive metacirculants

Cubic vertex‐transitive graphs of order 2pq

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