Folding of Cayley Graphs

[摘要] The aim of this paper is to discuss the folding of Cayley graphs of finite group.We prove that, for any finite group G,|G|=n and H is a subgroup of G. Then Cayley graph Γ=Cay(G,S) of G with respect to S=H\{1G} can be folded into a complete graph K, where r=|H|. Hence every Cayley graph Γ=Cay(G,S) of valency n-1 can not be folded. Also every Cayley graph Γ=Cay(G,S) of valency one can be folded and Γ=Cay(G,S), where S is generating set, every elements in it is self inverse and | |= 1 | | 2 SG, can be folded to an edge. Theorems governing these types of foldings are achieved.

[关键词] Cayley graph;Folding;Graph folding;Applied mathematic