A graph is symmetric if its automorphism group acts transitively on both the vertex and the arc sets. Stimulated by Lorimer's work on symmetric graphs of prime valency, we make a further investigation on the structural properties of the automorphism groups of connected symmetric graphs with prime valency. Also, as an application, we give a classification for symmetric graphs of prime valency arising from a class of almost simple groups.

中文翻译：

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与一些几乎简单的群相关的素价的对称图

如果一个图的自同构群在顶点集和弧集上都具有传递性，则该图是对称的。受 Lorimer 对质价对称图工作的启发，我们进一步研究了质价连通对称图的自同构群的结构性质。此外，作为一个应用，我们对由一类几乎单群产生的素价对称图进行分类。