Finite groups admitting a connected cubic integral bi-Cayley graph

Document Type : Research Paper


1 University of Larestan

2 Department of mathematical sciences Isfahan University of Technology Isfahan, Iran.



A graph   is called integral if all eigenvalues of its adjacency matrix  are integers.  Given a subset $S$ of a finite group $G$, the bi-Cayley graph $BCay(G,S)$ is a graph with vertex set $G\times\{1,2\}$ and edge set $\{\{(x,1),(sx,2)\}\mid s\in S, x\in G\}$.  In this paper, we classify all finite groups admitting a connected cubic integral bi-Cayley graph.


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