4p阶三度点传递图

Cubic Vertex-Transitive Graphs of Order 4p

一个图称为点传递图或对称图如果它的自同构群分别在点集或点集有序对上传递.设p为素数,给出了4p阶连通三度点传递图分类(徐明曜等在[Chin.Ann.Math.,2004,25B(4):545-554]中分类了4p阶连通三度对称图).确定了4p阶互不同构的连通三度点传递图的个数f(4p);当p=2,3,5,7时,f(4p)分别为2,4,8,6;当p≥11且4|(p-1)时,f(4p)=5+2/(p-3);当p≥11且4(p-1)时,f(4p)=3+2/(p-3).

A graph is vertex-transitive or symmetric if its automorphism group acts transitively on vertices or ordered adjacent pairs of the graph respectively. Let p be a prime. Xu et al. [Chin. Ann. Math., 2004, 25B（4）：545-554] classified the connected cubic symmetric graphs of order 4p. This paper gives a classification of connected cubic vertex-transitive graphs of order 4p. As a result, the number of pairwise non-isomorphic connected cubic vertex-transitive graph of order 4p is 2 for p = 2, 4 for p = 3, 8 for p = 5, 6 for p = 7, 5＋p-3/2 for p≥11 with4｜ （P-1） and3＋p-3/2 forp≥11with4｜（p-1）.