On Spectrum of Neighbourhood Corona Product of Signed Graphs

Abstract

Given two signed graphs ${\Gamma }_1$ with nodes $\{u_1,u_2,\cdots ,u_n\}$ and ${\Gamma }_2$, the neighbourhood corona, ${\Gamma }_1\ast {\Gamma }_2$ is the signed graph obtained by taking one copy of ${\Gamma }_1$ and $n_1$ copies of ${\Gamma }_2$, and joining every neighbour of the $i^{th}$ node with each nodes of the $i^{th}$ copy of ${\Gamma }_2$ by a new signed edge. In this paper we will determine the condition for ${\Gamma }_1\ast {\Gamma }_2$ to be balanced. We also determine the adjacency spectrum of ${\Gamma }_1\ast {\Gamma }_2$ for arbitrary ${\Gamma }_1$ and ${\Gamma }_2$, and Laplacian and signless Laplacian spectrum of ${\Gamma }_1\ast {\Gamma }_2$ for regular ${\Gamma }_1$ and arbitrary ${\Gamma }_2$, in terms of the corresponding spectrum of ${\Gamma }_1$ and ${\Gamma }_2$.

References in corpus (1)

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

Cited by in corpus (1)

• On Spectral Graph Determination