The spectral determinations of some classes of multicone graphs

Abstract

The main goal of the work is to characterize new families of multicone graphs which are determined by their spectra. A multicone graph is obtained from the join of a clique and a regular graph. Let n be a natural number, the friendship graph consists of n edge-disjoint triangles that all of them have only one in common vertex. In this paper, we present new classes of multicone graphs that friendship graphs are special classes of them and we show these graphs and their complements are determined by their adjacency spectra as well as their Laplacian spectra. It is proved that complement of special families of these graphs, are determined by their adjacency spectra. Additionally, we prove that graphs cospectral with these graphs are perfect.