ECCENTRIC CONNECTIVITY INDEX AND ECCENTRIC DISTANCE SUM OF SOME GRAPH OPERATIONS

Let G = (V;E) be a connected graph. The eccentric connectivity index of G, c(G), is defined as c(G) = Pv2V (G) deg(v)ec(v), where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. The eccentric distance sum of G is defined as d(G) = Pv2V (G) ec(v)D(v), where D(v) = Pu2V (G) d(u; v). In this paper, we calculate the eccentric connectivity index and eccentric distance sum of generalized hierarchical product of graphs. Moreover, we present the exact formulae for the eccentric connectivity index of F-sum graphs in terms of some invariants of the factors.