The Minimum Spectral Radius of Signless Laplacian of Graphs with a Given Clique Number

Abstract In this paper we observe that the minimal signless Laplacian spectral radius is obtained uniquely at the kite graph PKn−ω,ω among all connected graphs with n vertices and clique number ω. In addition, we show that the spectral radius μ of PKm,ω (m ≥ 1) satisfies More precisely, for m > 1, μ satisfies the equation where and . At last the spectral radius μ(PK∞,ω) of the infinite graph PK∞,ω is also discussed.