The spectral determination of the multicone graphs Kw+P

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.

arXiv commentThis paper characterizes new classes of multicone graph. Note that:In (V_7) Lemma 3.1 and Remark 1 modified and also I noted Lemmas 2.2 and 2.9 are the same. So, I deleted one of them. This version is the final. arXiv admin note: text overlap with arXiv:1703.08728