On the spectral radius and energy of the degree distance matrix of a connected graph

Abstract Let G G be a simple connected graph on n n vertices. The degree of a vertex v ∈ V (G) v V (G), denoted by d v dₕ, is the number of edges incident with v v and the distance between any two vertices u, v ∈ V (G) u, v V (G), denoted by d u v dₔₕ, is defined as the length of the shortest path from u u to v v. The distance matrix of G G, denoted by, D (G) D (G), is defined as D (G) = d u v D (G) =dₔₕ. We now define and investigate the degree distance matrix of a connected graph G G, defined as <jats: inline-graphic xm