The infinitude of 7-arc-transitive graphs

Marston Conder and Cameron Walker

Abstract

In this paper it is shown that for all but finitely many
positive integers $n$, there is a finite connected
7-arc-transitive quartic graph with the alternating group
$A_n$ acting transitively on its 7-arcs, and another with the
symmetric group $S_n$ acting transitively on its 7-arcs.
The proof uses a construction involving permutation
representations to obtain finite graphs with the desired
property.

Keywords
graph, symmetry, automorphism group

Math Review Classification
Primary 05C25 ; Secondary 20B25

Last Updated
June 1998

Length
13 pages

Availability
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