Title: A CLASSIFICATION OF FINITE GROUPS WITH INTEGRAL BI-CAYLEY GRAPHS
Abstract: The bi-Cayley graph of a finite group $G$ with respect to a subset $Ssubseteq G$, which is denoted by $BCay(G,S)$, is the graph with vertex set $Gtimes{1,2}$ and edge set ${{(x,1), (sx,2)}mid xin G, sin S}$. 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 $S_3$.
Publication Year: 2015
Publication Date: 2015-12-01
Language: en
Type: article
Access and Citation
Cited By Count: 4
AI Researcher Chatbot
Get quick answers to your questions about the article from our AI researcher chatbot