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, ‎\xi^{c}(G)‎, ‎is defined as‎ ‎\xi^{c}(G)=\sum_{v\in V(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 \xi^{d}(G)=\sum_{v\in‎ ‎V(G)}ec(v)D(v)‎, ‎where D(v)=\sum_{u\in V(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.

Keywords:

‎Eccentric connectivity index , eccentric distance sum , generalized hierarchical product , F-sum graphs