Automorphisms and isomorphisms of heptavalent symmetric graphs of order 32p

Abstract

A graph is symmetric if its automorphism group acts transitively on the set of arcs of the graph. In this paper, we determine the automorphisms and isomorphisms of connected heptavalent symmetric graphs of order \(32_p\) for each prime p. As a result, we get the complete classification of such graphs, and there are two sporadic such graphs with p = 2 and 3.