HS-integral and Eisenstein integral mixed Cayley graphs over abelian groups

A mixed graph is called second kind hermitian integral (or HS-integral) if the eigenvalues of its Hermitian-adjacency matrix of second kind are integers. A mixed graph is called Eisenstein integral if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. Let Γ be an abelian group....

Full description

Saved in:
Bibliographic Details
Published in:Linear algebra and its applications 2022-07, Vol.645, p.68-90
Main Authors: Kadyan, Monu, Bhattacharjya, Bikash
Format: Article
Language:English
Subjects:
Eigenvalues
Eisenstein integral mixed graph
Group theory
Hermitian adjacency matrix of second kind
HS-integral mixed graph
Integers
Linear algebra
Mixed Cayley graph
Citations: Items that this one cites
Items that cite this one
Online Access:Get full text
Tags: Add Tag
No Tags, Be the first to tag this record!
Description
Summary:A mixed graph is called second kind hermitian integral (or HS-integral) if the eigenvalues of its Hermitian-adjacency matrix of second kind are integers. A mixed graph is called Eisenstein integral if the eigenvalues of its (0, 1)-adjacency matrix are Eisenstein integers. Let Γ be an abelian group. We characterize the set S for which a mixed Cayley graph Cay(Γ,S) is HS-integral. We also show that a mixed Cayley graph is Eisenstein integral if and only if it is HS-integral.
ISSN:0024-3795
1873-1856
DOI:10.1016/j.laa.2022.03.008