Abstract
A multicone graph is defined to be the join of a clique and a regular graph. Let w, n and m be natural numbers, and let Kw and Kn,n denote a complete graph and a complete bipartite graph, respectively. In this work, it is proved that connected multicone graphs Kw▽mKn,n, natural generalizations of friendship graphs, are determined by their adjacency spectra as well as their Laplacian spectra. Also, we show that the complement of multicone graphs Kw▽Kn,n is determined by their adjacency spectra. Furthermore, we prove that any graph cospectral with a multicone graph Kw▽mKn,n is perfect with respect to its adjacency (Laplacian) spectra. At the end of the paper, we pose two problems for further research.
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