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.
Stevanović, D., & Hansen, P. (2008). The minimum spectral radius of graphs with a given clique number. Electronic Journal of Linear Algebra, 17, 110–117. https://doi.org/10.13001/1081-3810.1253