Bounds on the difference between the eccentric distance sum and the degree distance of graphs

The eccentric distance sum and degree distance have been well-studied in the past several years. More recently, many authors have considered the relationships between several distance-based graph invariants. Hua et al. 9 investigated the relationship between the eccentric distance sum ?d (G) and the degree distance D?(G) of a graph G. In this paper, we give some further results on ?d(G)-D?(G). Firstly, we determine upper and lower bounds on ?d(G)-D?(G) among general connected graphs in terms of the number of cut edges, and characterize the corresponding extremal graphs. Meanwhile, we identify the extremal graphs of given girth g having the minimum and maximum ?d (G)-D?(G). Secondly, we consider the extremal problems among bipartite graphs on ?d(G)-D?(G) in terms of matching number. And then we characterize the extremal bipartite graphs with diameter d having minimum ?d(G)-D?(G).