The minimum spectral radius of graphs with a given clique number

Abstract

In this paper, it is shown that among connected graphs with maximum clique size ω, the minimum value of the spectral radius of adjacency matrix is attained for a kite graph PKn-ω,ω, which consists of a complete graph Kω to a vertex of which a path P n-ω is attached. For any fixed ω, a small interval to which the spectral radii of kites PKm,ω, m ≥ 1, belong is exhibited.