The matchings and spectral radius of graphs involving minimum degree.

Let n ≥ 29 , k ≥ 2 and δ ≥ 1 be three positive integers, where n ≥ k + 2 and n ≡ k (mod 2). In this paper, we characterize the extremal graphs with maximum spectral radius among all connected graphs on n vertices with minimum degree δ and matching number at most n − k 2. This solves an open problem proposed in [10]. [ABSTRACT FROM AUTHOR]