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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 P K n−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 P Km,ω, m ≥ 1, belong is exhibited. http://math.technion.ac.il/iic/ela From the proof of Lemma 2.1, it is evident that P S u (λ) > P S v (λ) for all λ > ρ(S vdoi:10.13001/1081-3810.1253 fatcat:2txm6phfwfdepprgkrmi4rf2xy