Structural balance and spectral properties of generalized corona product of signed graphs

TL;DR

This paper extends the concept of corona product to signed graphs, analyzing their structural balance and spectral properties, and deriving formulas for various graph polynomials with conditions for co-spectrality.

Contribution

It introduces the generalized corona product of signed graphs and provides explicit formulas for their spectral polynomials and conditions for co-spectrality.

Findings

Derived formulas for characteristic, Laplacian, and signless Laplacian polynomials.

Established conditions for co-spectrality of generalized corona products.

Analyzed structural balance in the context of generalized corona products.

Abstract

In this paper, we extend our earlier proposal of corona product of signed graphs into generalized corona product of signed graphs inspired by the generalized corona product of unsigned graphs. Then we study structural balance and spectral properties of these graphs. Utilizing the notion of coronal of a graph, we determine computable formulae of characteristic, Laplacian, and signless Laplacian polynomials of generalized corona product of signed graphs. Finally, we provide sufficient conditions for the generalized corona product of some distinct collections of signed graphs to be co-spectral.