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

For a connected graph G, let (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 (G). An odd 1, b -factor of a graph G is a spanning subgraph G₀ such that the degree d₆䃐 (v) of v in G₀ is odd and 1 d₆䃐 (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 (G) > n-k2 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.