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 G₀ such that the degree d_G0 (v) of v in G₀ is odd and 1 ≤ d_G0 (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 in an n-vertex t-connected graph G, 2 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.