Tetravalent half-arc-transitive graphs of order 8p

Abstract

A graph is half-arc-transitive if its automorphism group acts transitively on its vertex set, edge set, but not arc set. Let p be a prime. It is known that there exist no tetravalent half-arc-transitive graphs of order p or 2 p. Feng et al. (J Algebraic Combin 26:431-451, 2007) gave the classification of tetravalent half-arc-transitive graphs of order 4 p. In this paper, a classification is given of all tetravalent half-arc-transitive graphs of order 8 p.

Tetravalent half-arc-transitive graphs of order $12p$

“…In [10] a complete classification of tetravalent half-arc-transitive metacirculants of order 2-powers was given. In [36], a classification of all tetravalent half-arc-transitive graphs of order 8p was given. In this paper, we will study tetravalent half-arc-transitive graphs of order 12p.…”