BOUNDS FOR DEGREE DISTANCE OF A GRAPH

Let G be a simple connected graph with vertex set V(G), then the degree distance of G, D'(G), is defined as D'(G) = Sigma(x is an element of V(G)) d(x) Sigma(y is an element of V(G)) d(x,y), where d(x) and d(x, y) are the degree of x and the distance between x and y, respectively. In this paper, lower and upper bounds on D'(G) are obtained in terms of various graphical parameters like first Zagreb index, order, size, diameter, radius, minimum degree, and graphs for which these bounds are attained are characterized.