The Normality And Ci Property Of 4-valent Cayley Graphs Of Dihedral Groups Of Order 32p

A Cay-ley graph ?:=Cay((G,S)of the group G with its subset S(?)1 is said to be normal if R(G)?the group of right multiplications is normal in Aut(?);The graph ? is said Graph Regular Representation(GRR)if R(G)=Aut(?)and ? is undirected.In this paper,some research methods and techniques of algebra graph theory are used to study the related properties of small valent Cayley graphs on dihedral groups and the CI property of the group by combining the knowledge of group theory.In the third chapter of this paper,we research the normality of connected 4-valent undirected Cayley graphs of dihedral groups of order 32p,G?(a,b|a16p=b2=1,ab=?-1>,where p is an odd prime.Firstly?the 4-variable self-inverse generated subset S of G#is divided into seven types under the action of Aut(G);We study the related properties of connected 4-valent undirected Cayley graphs composed of these seven classes of S,and obtain rich and meaningful results,including the infinite family of 4-valent GRR of the group.In the fourth chapter of this paper,we research the CI property of 3-,4-variable self-inverse generated subset of connected undirected Cayley graph of dihedral groups of order 32p,G=(a,b | a16P=b2=1,ab=a-1),where p is an odd prime.Then we completely solve the problem for CI property of 3-variable self-inverse generated subset,and determine the infinite families of a group of 4-element(strong)CI.