On the minimal eccentric connectivity indices of graphs

Abstract: Let be a simple connected graph. The eccentric connectivity index of is defined as , where the eccentricity is the largest distance between and any other vertex of . In this paper, we obtain lower bounds on in terms of the number of edges among -vertex connected graphs with given diameter. Over connected graphs on vertices with edges and diameter at least , and connected graphs on vertices with diameter at least , we provide lower bounds on and characterize the extremal graphs, respectively. [Copyright &y& Elsevier]