An automorphism ρ of a graph X is said to be semiregular provided all of its cycles in its cycle decomposition are of the same length, and is said to be simplicial if it is semiregular and the quotient multigraph $X_{\rho }$ of X with respect to ρ is a simple graph, and thus of the same valency as X. It is shown that, with the exception of the complete graph $K_4$, the Petersen graph, the Coxeter graph and the so called H-graph (alternatively denoted as $S(17)$, the smallest graph in the family of the so called Sextet graphs $S(p)$, $p\equiv \pm 1(\mathrm{mod}16)$), every cubic arc-transitive graph with a primitive automorphism group admits a simplicial automorphism.

中文翻译：

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通过单纯自同构的图中的对称性

如果图X的自同构ρ在其循环分解中的所有循环都具有相同的长度，则称其为半正规的，并且如果它是半正规且商多重图则称其为单纯的$X_{\rho }$X与ρ的关系是一个简单的图，因此与X具有相同的化合价。可以看出，除了全图${ķ}_4$、Petersen 图、Coxeter 图和所谓的 H 图（也可以表示为$\mathrm{小号}(17)$, 所谓的六重图家族中最小的图$\mathrm{小号}(p)$,$p\equiv \pm 1(\mathrm{模组}16)$)，每个具有原始自同构群的三次弧传递图都承认单纯自同构。