Cubic Sign Cayley Graph

Let X=Cay(G,S)be the Cayley graph generated by subset S of group G,and S=S-1.Define the sign function ?:(si,sig)? {+1,-1} if ?satisfies ?(si)=?(si-1),?=Cay(G,S,?)is the sign Cayley graph on G with respect to S.This paper mainly focuses on the spectrum of the 3 degree sign Cayley graph,first gives the spectrum of the sign Cayley graph on the cyclic group,gives the connectivity condition of the 3 degree sign Cayley graph on the cyclic group,and obtains the energy problem of the 3 degree sign Cayley graph on the cyclic group.Second,the integral spectrum problem of the small valent sign Cayley graph is discussed,and the relationship between the integral spectrum sign Cayley graph and the integral spectrum Cayley graph is obtained under the condition of small valent.