Abstract
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.
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