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 PK_n-ω,ω, consists of a complete graph K_ω 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 PK_m,ω, m≥1, belong is exhibited.