On the spectral radius of graphs without a star forest

Abstract Let F = ∪ i = 1 k S d i be the union of pairwise vertex-disjoint k stars of order d 1 + 1 , … , d k + 1 , respectively, where k ≥ 2 and d 1 ≥ ⋯ ≥ d k ≥ 1 . In this paper, we present two sharp upper bounds for the spectral radius of F -free (bipartite) graphs and characterize all corresponding extremal graphs. Moreover, the minimum least eigenvalue of the adjacency matrix of an F -free graph and all extremal graphs are obtained.

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