Star complements in signed graphs with two symmetric eigenvalues

DOI: 10.48129/kjs.12619

Authors

DOI:

https://doi.org/10.48129/kjs.12619

Abstract

We consider signed graphs $G$ whose spectrum is comprised of exactly two (distinct) eigenvalues that differ only in sign, abbreviated to signed graphs with two symmetric eigenvalues. We obtain some relationships between such signed graphs and their star complements. Our results include structural examinations and constructions of infinite families of signed graphs with two symmetric eigenvalues. We also determine the bases for the eigenspaces of the eigenvalues of $G$ in terms of the eigenspaces of its star complement. In particular, we consider the case in which a star complement has two symmetric eigenvalues, as well.

Author Biography

Assoc. Prof, Zoran Stanić, University of Belgrade

Faculty of Mathematics

Associate Professor

Published

26-12-2021

Issue

Section

Mathematics