Matching, odd [1,b]-factor and distance spectral radius of graphs with given some parameters

For a connected graph G , let μ(G) denote 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 α(G) . An odd [1,b] -factor of a graph G is a spanning subgraph G_0 such that the degree dG_0(v) of v in G_0 is odd and 1 ≤ dG_0(v) ≤ b for every vertex v ∈ V(G) . In this paper, we give a sharp upper bound in terms of the distance spectral radius to guarantee α(G) > n-k/2 in an n -vertex t -connected graph G , where 2 ≤ k ≤ n-2 is an integer. We also 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 δ .