The minimum spectral radius of graphs with a given clique number
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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 PKn-ω,ω, consists of a complete graph Kω to a vertex of which a path Pn-ω is attached. For any fixed ω, a small interval to which the spectral radii of kites PKm,ω, m≥1, belong is exhibited.
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