Which Cayley Graphs are Integral?

A. Abdollahi, E. Vatandoost

Abstract


Let $G$ be a non-trivial group, $S\subseteq G\setminus \{1\}$ and $S=S^{-1}:=\{s^{-1} \;|\; s\in S\}$. The Cayley graph of $G$ denoted by $\Gamma(S:G)$ is a graph with vertex set $G$ and two vertices $a$ and $b$ are adjacent if $ab^{-1}\in S$. A graph is called integral, if its adjacency eigenvalues are integers. In this paper we determine all connected cubic integral Cayley graphs. We also introduce some infinite families of connected integral Cayley graphs.


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