Signed graphs with strong anti-reciprocal eigenvalue property

Abstract

The ordered pair , where G is an underlying graph and is a signature function, is called a signed graph. A nonsingular signed graph is said to satisfy strong reciprocal (or strong anti-reciprocal) eigenvalue property if for each eigenvalue there exists (or ) in the spectrum of 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.