Integral mixed cayley graph over abelian group

TL;DR

This paper characterizes when mixed Cayley graphs over abelian groups are integral by analyzing their Hermitian adjacency matrices and symbol sets, contributing to spectral graph theory.

Contribution

It provides a characterization of integral mixed Cayley graphs over abelian groups based on their symbol sets, advancing understanding of their spectral properties.

Findings

Characterization of integral mixed Cayley graphs over abelian groups

Conditions on symbol sets for integrality of eigenvalues

Extension of spectral graph theory to mixed Cayley graphs

Abstract

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 \textit{mixed Cayley graph} $Cay(\Gamma,S)$ is a mixed graph on the vertex set $\Gamma$ and edge set $\{ (a,b): b-a\in S \}$, where $0\not\in S$. We characterize integral mixed Cayley graph $Cay(\Gamma,S)$ over abelian group in terms of its symbol set $S$.