The spectral determination of the multicone graphs Kw+P

TL;DR

This paper proves that certain multicone graphs, formed by joining a clique with the Petersen graph, are uniquely identified by their signless Laplacian, Laplacian, and adjacency spectra, advancing spectral graph theory.

Contribution

It establishes that multicone graphs Kw+P are uniquely determined by their spectra, a novel spectral characterization result for these graph classes.

Findings

Multicone graphs Kw+P are determined by their spectra.

Spectral characterization applies to signless Laplacian, Laplacian, and adjacency spectra.

Advances understanding of spectral graph determination for complex graph classes.

Abstract

The main aim of this study is to characterize new classes of multicone graphs which are determined by their signless Laplacian spectra, their Laplacian spectra and their adjacency spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let P and Kw denote the Petersen graph and a complete graph on w vertices, respectively. In this paper, we show that multicone graphs Kw+P are determined by their signless Laplacian spectra, their Laplacian spectra and their adjacency spectra. Keywords: DS graph; Multicone graph; Signless Laplacian spectrum; Petersen graph.