Eccentric connectivity index of unicyclic graphs with application to cycloalkanes

Let G be a simple connected molecular graph. The eccentric connectivity index ξ(G) is defined as equation, where deg(ν) denotes the degree of vertex v and ec(ν) is the largest distance between ν and any other vertex u of G. In this paper, we construct the general formulas for the eccentric connectivity index of unicyclic graphs with application to cycloalkanes.