On the distance spectral radius, fractional matching and factors of graphs with given minimum degree

A fractional matching of G is a function (Formula presented) such that (Formula presented) for any (Formula presented), where (Formula presented) and e is incident with vi. Let (Formula presented) denote the fractional matching number of G, which is defined as (Formula presented) is a fractional matching of G. Let (Formula presented) be a set of graphs, a (Formula presented)-factor of a graph G is a spanning subgraph of G such that each component of which is isomorphic to one of (Formula presented) In this paper, we first establish a sharp upper bound for the distance spectral radius to guarantee that (Formula presented) in a graph G of order n with given minimum degree, where (Formula presented) is an integer. Then we give a sharp upper bound on the distance spectral radius of a graph G with given minimum degree to ensure that G has a (Formula presented)-factor, where 3 (Formula presented) is an integer. Moreover, we obtain a sharp upper bound on the distance spectral radius for the existence of a (Formula presented)-factor with (Formula presented) in a graph G with given minimum degree.