On the spectral determinations of the connected multicone graphs $K_r▽s{K}_t$

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 $r$, $t$ and $s$ be natural numbers, and let $K_r$ denote a complete graph on $r$ vertices. It is proved that connected multicone graphs $K_r▽s{K}_t$, 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 $K_r▽s{K}_t$ are determined by their adjacency spectra, where $s\ne 2$.

A correction to Theorem 5.3