On the spectral determinations of the connected multicone graphs

Abstract

In this study we investigate the spectra of the family of connected multicone graphs. A multicone graph is defined to be the join of a clique and a regular graph. Let , and be natural numbers, and let denote a complete graph on vertices. It is proved that connected multicone graphs , 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 is determined by their adjacency spectra, where .

Keywords

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