The spectral determinations of the connected multicone graphs K w ▽ mP 17 and K w ▽ mS

Finding and discovering any class of graphs which are determined by their spectra is always an important and interesting problem in the spectral graph theory. The main aim of this study is to characterize two classes of multicone graphs which are determined by both their adjacency and Laplacian spectra. A multicone graph is defined to be the join of a clique and a regular graph. Let Kw denote a complete graph on w vertices, and let m be a positive integer number. In A.Z.Abdian (2016) it has been shown that multicone graphs Kw ▽ P17 and Kw ▽ S are determined by both their adjacency and Laplacian spectra, where P17 and S denote the Paley graph of order 17 and the Schläfli graph, respectively. In this paper, we generalize these results and we prove that multicone graphs Kw ▽mP17 and Kw▽mS are determined by their adjacency spectra as well as their Laplacian spectra.