Cubic symmetric graphs having an abelian automorphism group with two orbits

2013/05/06 by Hiroki Koike, Koike, Hiroki, István Kovács +1
Mathematics · #05C25 #20B25 #Combinatorics (math.CO) #FOS: Mathematics #math.CO #msc:05C25 #msc:20B25

paper · pdf · doi:10.48550/arxiv.1305.1190

Keywords: cubic symmetric graph, Haar graph, voltage graph. This papaer has been withdrawn by the author because it is an outdated version

arxiv created 2015/04/13 · arxiv updated 2015/04/14

Abstract

Finite connected cubic symmetric graphs of girth 6 have been classified by K. Kutnar and D. Marušič, in particular, each of these graphs has an abelian automorphism group with two orbits on the vertex set. In this paper all cubic symmetric graphs with the latter property are determined. In particular, with the exception of the graphs K₄, K_3,3, Q₃, GP(5,2), GP(10,2), F40 and GP(24,5), all the obtained graphs are of girth 6.

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