On spectrum of corona product of duplication signed graph and its application

Abstract

This paper introduces the concept of $\mu$-signed and duplication signed graphs and shows that both are always structurally balanced. Using the duplication signed graph, we define the corona product of the duplication signed graph (Duplication add vertex corona product and duplication vertex corona product) and explore their structural properties. Additionally, we provide the adjacency spectrum of both the products for any $\Gamma_1$ and $\Gamma_2$, and the Laplacian and signless Laplacian spectrum for regular $\Gamma_1$ and arbitrary $\Gamma_2$, in terms of the corresponding spectrum of $\Gamma_1$ and $\Gamma_2$. Finally, we discuss its application in generating integral and equienergetic signed graphs.