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In this study we investigate the spectra of the family of connected multiconegraphs. A multicone graph is defined to be the join of a clique and a regulargraph. Let $ r $, $ t $ and $ s $ be natural numbers, and let $ K_r $ denote acomplete graph on $ r $ vertices. It is proved that connected multicone graphs$ K_r\bigtriangledown sK_t $, a natural generalization of friendship graphs,are determined by their adjacency spectra as well as their Laplacian spectra.Also, we show that the complement of multicone graphs $ K_r\bigtriangledownsK_t $ are determined by their adjacency spectra, where $ s\neq 2 $.

On the spectral determinations of the connected multicone graphs $ K_r\bigtriangledown sK_t $