General eccentric distance sum of graphs

For a,b is an element of R, we define the general eccentric distance sum of a connected graph G as EDSa,b(G) = Sigma(v is an element of V (G))(ecc(G)(v))(a)(D-G(v))(b), where V (G) is the vertex set of G, ecc(G)(v) is the eccentricity of a vertex v in G, D-G(v) = Sigma(w is an element of V (G))d(G)(v,w) and d(G)(v,w) is the distance between vertices v and w in G. This index generalizes several other indices of graphs. We present some bounds on the general eccentric distance sum for general graphs, bipartite graphs and trees of given order, graphs of given order and vertex connectivity and graphs of given order and number of pendant vertices. The extremal graphs are presented as well.