Eccentric connectivity index in transformation graph Gxy+

Abstract

Abstract Let G be a connected graph with vertex set V(G)and edge set E(G). The eccentric connectivity index of G is defined as ∑ν∈V(G)ec(ν) deg(ν) \sum\limits_{\nu\in{\rm{V}}\left({\rm{G}}\right)}{{\rm{ec}}\left(\nu\right)\,{\rm{deg}}\left(\nu\right)} where ec(v) the eccentricity of a vertex v and deg(v)is its degree and denoted by ɛc(G). In this paper, we investigate the eccentric connectivity index of the transformation graph Gxy+.