一类3p^n阶亚循环群的4度Cayley图

Tetravalent Cayley Graphs on a Kind of Metacyclic Groups with Order 3p^n

采用群与图的方法,研究一类3pn阶亚循环群的连通4度无向Cayley图.通过决定Caley图的自同构群得出此类亚循环群是弱4-CI的,并由此给出3pn亚循环群的连通4度无向Cayley图的完全分类,最后证明此类图都正规而且非弧传递.

A kind of metacyclic groups with order 3p^n was researched by using the group-theoretic and graphic methods. Though determining the full automorphism groups of these Cayley graphs,we have that the group is a weak 4-CI group and then determine the complete classification of its connected tetravalent Cayley graphs. Finally,we prove that all these Cayley graphs are normal but no arc-transitive.