Tetravalent Normal Edge-transitive Cayley Graphs On Groups Of Order 6p~2

In the study of groups and graphs,the transitivity of graphs(vertex transitive,edge transitive,arc transitive)has always been the focus by many scholars.The transitivity of the graphs is mainly characterized by the full graph automorphism group,but it is a very difficult to solve the full graph automorphism group.Cayley graphs were proposed by A.Cayley in 1878.For the Cayley graph,assume ?=Cay(G,S),then Aut(?)? NAut(?)(G)=G(?)Aut(G,S).Therefore,Prof.Xu Mingyao put forward the concept of normal Cayley graph in 1998,that is,if G(?)Aut(?),then Aut(?)=NAut(r)(G)=G(?)Aut(G,S),and ?=Cay(G,S)is called a normal Cayley graph on the group G.After that,the study of Cayley graph is divided into two parts:normal and non-normal.C.E.Praeger first proposed the concept of normal edge-transitive Cayley graph in 1999,that is,if NAut(?)(G)is transitive on the set of edges of ?,then ?=Cay(G,S)is called a normal edge-transitive Cayley graph on the group G.In[2],the nec-essary and sufficient conditions are obtained for a Cayley graph to be normal edge-transitive.As a subclass of the edge-transitive Cayley graph,the normal edge-transitive Cayley graph has some good properties.Since then,normal edge-transitive Cayley graphs have received much attention:In 2013,M.R.Darafsheh and A.Assari determined the normal edge-transitive Cayley graphs on a non-abelian group of order 4p,where p is a prime;In 2017,Y.Pakravesh and A.Iranmanesh s-tudied the normal edge-transitive Cayley graphs on the non-abelian groups of order 4p2,where p is a prime.Based on the above result,this thesis studies the tetravalent normal edge-transitive Cayley graphs on groups of order 6p2,where p is an odd prime,p?3 and 3(?)(p-1).We apply the theory of groups deeply,especially permutation groups on this thesis.By using the interaction between groups and graphs,we give the structure of eight class of groups of order 6p2 firstly.Besides,we prove that there are two groups that have no tetravalent normal edge-transitive Cayley graphs.There are three groups which have tetravalent normal-arc transitive graphs.There are two groups which have normal 1/2-arc transitive Cayley graphs or normal-arc transitive Cayley graphs.There is a group which has only normal 1/2-arc transitive Cayley graphs.Finally,the full automorphism group of the graphs are analyzed in this thesis.