Tetravalent Normal Edge-transitive Cayley Graphs On Groups Of Order 8p

This thesis is devoted deliberating the tetravalent normal edge-transitive Cayley graphs on several families of groups of order 8p.Let ?=Cay(G,S)be a Cayley graph of group G with respect to S,where subset S contains no identity element.If the normalizer of G in Aut(?)is transitive on the edge set of ?,then ? is called a normal edge-transitive Cayley graphThe definition of normal edge-transitive Cayley graph was put forward by C.E Praeger in 1999[12],and the necessary and sufficient conditions for normal edge-transitive Cayley graphs were given.Ever since from then on,the normal edge-transitive Cayley graphs have been attracted much attention by algebraic scholars at home and abroad.For example,M.R.Darafsheh give the classification of normal edge-transitive Cayley graphs on a class of non-abelian group of order 4p in 2013 R.D.Mohammad and Y.Maysam discussed the tetravalent edge-transitive Cayley graphs on a class of group of order 6n in 2017Inspired by the above result.By analyzing the structure and automorphism of the six families groups of order 8p one by one.We prove that there are three groups which it is no tetravalent normal edge-transitive Cayley graphs.And there are three groups which it is tetravalent normal edge-transitive Cayley graphs.Furthermore the classification of these graphs and the characterization and analysis of the graph automorphism groups are obtained in the thesis.