Signed graphs with strong (anti-)reciprocal eigenvalue property

Abstract

A (signed) graph is said to exhibit the strong reciprocal (anti-reciprocal) eigenvalue property (SR) (resp., (-SR)) if for any eigenvalue λ\lambda , it has 1λ\frac{1}{\lambda } (resp.,−1λ-\frac{1}{\lambda }) as an eigenvalue as well, with the same multiplicity. It is well known that the corona of a (signed) graph does have the property -SR, and if the graph has symmetric spectrum, then it also has the property SR. Therefore, it is interesting to identify (signed) graphs which are not corona graphs with the properties SR or -SR. Recently, a few constructions for unsigned graphs with the property -SR have been offered. In this article, we extend such constructions to signed graphs.

Keywords

• adjacency spectrum
• corona product
• kronecker product
• subdivision
• 05c50
• 05c22