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Characterization of edge-transitive 4-valent bicirculants

✍ Scribed by István Kovács; Boštjan Kuzman; Aleksander Malnič; Steve Wilson

Book ID
102339847
Publisher
John Wiley and Sons
Year
2011
Tongue
English
Weight
262 KB
Volume
69
Category
Article
ISSN
0364-9024

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✦ Synopsis

Abstract

A bicirculant is a graph admitting an automorphism with exactly two vertex‐orbits of equal size. All non‐isomorphic 4‐valent edge‐transitive bicirculants are characterized in this article. As a corollary, a characterization of 4‐valent arc‐transitive dihedrants is obtained. © 2011 Wiley Periodicals, Inc. J Graph Theory.

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Let \(\Gamma\) be a connected, 4-valent, \(G\)-symmetric graph. Each normal subgroup \(N\) of \(G\) gives rise to a natural symmetric quotient \(\Gamma_{N}\), the vertices of which are the \(N\)-orbits on \(V \Gamma\). If this quotient \(\Gamma_{N}\) is not itself 4-valent, then it was shown in [1]