On the degree distance of a graph Original Research Article

If image is a connected graph with vertex set image, then the degree distance of image, image, is defined as image, where image is the degree of vertex image, and image denotes the distance between image and image. We prove the asymptotically sharp upper bound image for graphs of order image and diameter image. As a corollary we obtain the bound image for graphs of order image. This essentially proves a conjecture by Tomescu [I. Tomescu, Some extremal properties of the degree distance of a graph, Discrete Appl. Math. (98) (1999) 159–163].