The spectral characterization of the connected multicone graphs

Abstract

A multicone graph is defined to be the join of a clique and a regular graph. Let , and be natural numbers, and let and denote a complete graph and a complete bipartite graph, respectively. In this work, it is proved that connected multicone graphs , 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 is determined by their adjacency spectra. Furthermore, we prove that any graph cospectral with a multicone graph is perfect with respect to its adjacency (Laplacian) spectra. At the end of the paper, we pose two problems for further research.

Keywords

• adjacency spectrum
• laplacian spectrum
• multicone graph
• friendship graph
• ds graph