Spectra of new graph operations based on central graph

TL;DR

This paper introduces new graph operations based on the central graph concept and analyzes their spectra, providing methods to generate cospectral graphs and calculating key graph invariants.

Contribution

It defines central vertex, edge corona, and edge neighborhood corona operations and determines their spectra, enabling the construction of infinitely many cospectral graphs.

Findings

Derived spectra for new graph operations.

Constructed infinitely many cospectral graph pairs.

Calculated spanning trees and Kirchhoff index for these graphs.

Abstract

In this paper, we introduce central vertex corona, central edge corona, and central edge neighborhood corona of graphs using central graph. Also, we determine their adjacency spectrum, Laplacian spectrum and signless Laplacian spectrum. From our results, it is possible to obtain infinitely many pairs of adjacency (respectively, Laplacian and signless Laplacian) cospectral graphs. As an application, we calculate the number of spanning trees and the Kirchhoff index of the resulting graphs.