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 2p. Feng et al. (J Algebraic Combin 26:431–451, 2007) gave the classification of tetravalent half-arc-transitive graphs of order 4p. In this paper, a classification is given of all tetravalent half-arc-transitive graphs of order 8p.

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8 p阶四价半弧传递图

如果图形的自同构组在其顶点集，边集而非圆弧集上传递传递，则该图是半弧传递的。令p为质数。已知不存在p或2 p阶的四价半弧传递图。冯等。（J Algebraic Combin 26：431–451，2007）给出了4 p阶四价半弧传递图的分类。在本文中，给出了所有8 p阶四价半弧传递图的分类。