Adjacency spectral characterization of the graphs Kw 5 P17 and Kw 5 S

Abstract

In A.Z. Abdian, Two classes of multicone graphs determined by their spectra, J. Math. Ext., 10 (2016), 111–121, it was conjectured that the complement of the multicone graphs, the join of a clique and a regular graph, Kw 5P17 and Kw 5S, are determined by their adjacency spectra, where P17 and S denote the Paley graph of order 17 and the Schlafli graph, ¨ respectively. In this article, we aim to answer to these conjectures.