Pentavalent symmetric graphs of order \(30p\)

Authors

  • B. Ling Yunnan University
  • C. X. Wu Yunnan University
  • B. Lou Yunnan University

Keywords:

arc-transitive graph, normal quotient, automorphism group

Abstract

A complete classification is given of pentavalent symmetric graphs of order \(30p\), where \(p⩾5\) is a prime. It is proved that such a graph \(Γ\) exists if and only if \(p=13\) and, up to isomorphism, there is only one such graph. Furthermore, \(Γ\) is isomorphic to \(C\)390, a coset graph of PSL(2, 25) with \(AutΓ=PSL(2, 25)\), and \(Γ\) is \(2\)-regular. The classification involves a new \(2\)-regular pentavalent graph construction with square-free order. DOI:- 10.1017/S0004972714000616

Published

2014-09-20

Issue

Vol. 90 No. 3 (2014)

Section

Articles
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