The Eccentric Connectivity Index of Some Special Graphs

If g is a connected graph with vertex set v, then the eccentric connectivity index of g, ?^c (g), is defined as ?_(v?v)??deg?(v)ecc(v)? where deg?(v) is the degree of a vertex v and ecc(v) is its eccentricity. let a, b and c are families of graphs made by joining p_n to k_m, made by putting k_minstead of each vertex in p_n and made by putting c_m instead of each vertex in p_n, respectively. in this paper we compute the eccentric connectivity index of these families of graphs.