  Let $\mu(G)$ denote the the distance spectral radius of $G$. A matching in a
graph $G$ is a set of disjoint edges of $G$. The maximum size of a matching in
$G$ is called the matching number of $G$, denoted by $\alpha(G)$. In this
paper, we give a sharp upper bound in terms of the distance spectral radius to
guarantee $\alpha(G)>\frac{n-k}{2}$ in a graph $G$ with given connectivity.
  Let $a$ and $b$ be two positive integers with $a\le b$. An $[a, b]$-factor of
a graph $G$ is a spanning subgraph $G_0$ such that for every vertex $v\in V
(G)$, the degree $d_{G_0}(v)$ of $v$ in $H$ satisfies $a\le d_{G_0}(v)\le b$.
In this paper, we present a sharp upper bound in terms of distance spectral
radius for the existence of an odd $[1,b]$-factor in a graph with given minimum
degree $\delta$.
