A classification of finite groups with integral bi-Cayley graphs
نویسندگان
1 Department of Mathematics, Isfahan University of Technology, Isfahan, Iran
2 Departmant of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran
doi
10.22108/toc.2015.7807چکیده
The bi-Cayley graph of a finite group $G$ with respect to a subset $S\subseteq G$, which is denoted by $BCay(G,S)$, is the graph with vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1), (sx,2)\}\mid x\in G, \ s\in S\}$. A finite group $G$ is called a \textit{bi-Cayley integral group} if for any subset $S$ of $G$, $BCay(G,S)$ is a graph with integer eigenvalues. In this paper we prove that a finite group $G$ is a bi-Cayley integral group if and only if $G$ is isomorphic to one of the groups $\Bbb Z_2^k$, for some $k$, $\Bbb Z_3$ or $S_3$.
