Some Algebraic Properties of Bi-Cayley Graph


Hua Zou and Jixiang Meng
College of Mathematics and Systems Science, Xinjiang University, Xinjiang 830046, P. R. China


Abstract     Full Text  PPT

For a finite group $G$ and a subset $S$ (possibly, contains the identity element)of $G$, the Bi-Cayley graph $X=BC(G,S)$ of $G$ with respect to $S$ is defined as the bipartite graph with vertex set $G\times\{0,1\}$ and edge set $\{\{(g,0),(sg,1)\}|g\in G,s\in S\}$. In this paper, we investigate the relation between the eigenvalues of Cayley graph $D(G,S)$ and $BC(G,S)$ for finite abelian group $G$. As a consequence, we determine the eigenvalues of Bi-Cayley graphs of cyclic groups. In addition, some asymptotic enumeration theorems are presented.