Eccentric connectivity index of identity graph of cyclic group and finite commutative ring with unity

Abstract

Research on graph associated with a finite algebraic structure has attracted many attentions. On the other hand, eccentric connectivity index is an interesting topic and many studies have been reported. For simple connected graph G, let e(v) denoted the eccentricity of vertex v and deg(v) denoted the degree of vertex v in G. Eccentric connectivity index of G is defined as the sum of all e(v)deg(v), for any v in G. We focus the study on determining eccentricity connectivity index of identity graph of cyclic group and finite commutative ring with unity. We present the exact formula for eccentricity connectivity index of identity graph of these two algebraic structures.