Integral Mixed Cayley Graphs over Abelian Groups

A mixed graph is said to be integral if all the eigenvalues of its Hermitian adjacency matrix are integer. Let $\Gamma$ be an abelian group. The mixed Cayley graph $Cay(\Gamma,S)$ is a mixed graph on the vertex set $\Gamma$ and edge set $\left\{ (a,b): b-a\in S \right\}$, where $0\not\in S$. We char...

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Bibliographic Details
Published in:The Electronic journal of combinatorics 2021-12, Vol.28 (4)
Main Authors: Kadyan, Monu, Bhattacharjya, Bikash
Format: Article
Language:English
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Summary:A mixed graph is said to be integral if all the eigenvalues of its Hermitian adjacency matrix are integer. Let $\Gamma$ be an abelian group. The mixed Cayley graph $Cay(\Gamma,S)$ is a mixed graph on the vertex set $\Gamma$ and edge set $\left\{ (a,b): b-a\in S \right\}$, where $0\not\in S$. We characterize integral mixed Cayley graph $Cay(\Gamma,S)$ over an abelian group $\Gamma$ in terms of its connection set $S$.
ISSN:1077-8926
1077-8926
DOI:10.37236/10534