Eccentric Connectivity Index And Eccentric Distance Sum Of Graph Operations

The study of topological indices of graphs is a very important part of graph theory.In general, a topological index, sometimes also known as a graph-theoretic index, is anumerical invariant of a graph. There are several topological indices have been definedsuch as, wiener index W, hyper-Wiener index W W, PI index, Hosoya index, ABC index,Wiener polarity index, Szeged index, eccentric connectivity index and eccentric distancesum. Many of them have been applied as means for modeling chemical, pharmaceuticaland other properties of molecules.The eccentric connectivity index of G, ξ~c(G), is defined as ξ~c(G)=v∈V (G)d(v)ec(v),where d(v) is the degree of a vertex v and ec(v) is its eccentricity. The eccentric distancesum of G is defined as ξ~d(G)=v∈V (G)ec(v)D(v), where D(v)=u∈V (G)d(u, v). Inthis paper, we calculate the eccentric connectivity index and eccentric distance sum ofgeneralized hierarchical product of graphs. Moreover, we present the exact formulaefor the eccentric connectivity index of F-sum graphs in terms of some invariants of thefactors. Further more, the eccentric connectivity index of benzenoid parallelogram Bm,nare computed.