Ordering connected graphs having small degree distances

The concept of degree distance of a connected graph image is a variation of the well-known Wiener index, in which the degrees of vertices are also involved. It is defined by image, where image and image are the degree of image and the distance between image and image, respectively. In this paper it is proved that connected graphs of order image having the smallest degree distances are image and image (in this order), where image denotes the bistar consisting of vertex disjoint stars image and image with central vertices joined by an edge.