Connectivity of Bi-Cayley Graphs

Abstract

Let $G$ be a finite group and $S$ be a subset (possibly containing the identity element) of $G$. We define the Bi-Cayley graph $X=BC(G,S)$ to be the bipartite graph with vertices $G\times \{0,1\}$ and edges $\{(g,0),(sg,1):g\in G,s\in S\}$. In this paper, we show that if $X=BC(G,S)$ is connected, then $\kappa (X)=\delta (X)$.