Spectral characterization of multicone graphs

A multicone graph is defined to be the join of a clique and a regular graph. Based on Zhou and Cho’s result [ B. Zhou, H.H. Cho , Remarks on spectral radius and Laplacian eigenvalues of a graph, Czech. Math. J. 55 ( 130 ) (2005), 781–790], the spectral characterization of multicone graphs is investigated. Particularly, we determine a necessary and sufficient condition for two multicone graphs to be cospectral graphs and investigate the structures of graphs cospectral to a multicone graph. Additionally, lower and upper bounds for the largest eigenvalue of a multicone graph are given.