University of Isfahan Transactions on Combinatorics 2251-8657 4 4 2015 12 01 A classification of finite groups with integral bi-Cayley graphs 55 61 7807 10.22108/toc.2015.7807 EN Majid Arezoomand Departmant of Mathematical Sciences, Isfahan University of Technology, Isfahan, Iran Bijan Taeri Department of Mathematics, Isfahan University of Technology, Isfahan, Iran Journal Article 2014 07 14 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 $S_3$‎. https://toc.ui.ac.ir/article_7807_741eee48891d7eafd3a189c9e3afd5fb.pdf