Signed graphs with strong anti-reciprocal eigenvalue property

Abstract

The ordered pair $\widehat{G}=(G,\sigma )$, where G is an underlying graph and $\sigma :E(G)\to \{\pm 1\}$ is a signature function, is called a signed graph. A nonsingular signed graph $\widehat{G}$ is said to satisfy strong reciprocal (or strong anti-reciprocal) eigenvalue property if for each eigenvalue $\alpha$ there exists $\frac{1}{\alpha }$ (or $-\frac{1}{\alpha }$) in the spectrum of $\widehat{G}$ having same multiplicities, if we remove this multiplicity constraint then the signed graph is said to satisfy reciprocal (respectively anti-reciprocal) eigenvalue property. In this article, we investigate strong anti-reciprocal eigenvalue property in some families of signed graphs.

KEYWORDS:

• Corona and non-corona graphs
• signed graphs
• strong anti-reciprocal eigenvalue property
• strong reciprocal eigenvalue property

2020 MATHEMATICS SUBJECT CLASSIFICATION:

• 05C50
• 15A18

Disclosure statement

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.