Polynomial interpolation can be used to obtain closed formulas for topological indices of infinite series of molecular graphs. The method is discussed and its advantages and limitations are pointed out. This is illustrated on fullerenes C12k+4 and four topological indices: the Wiener index, the edge Wiener index, the eccentric connectivity index, and the reverse Wiener index. The results for th...

If G is a connected graph with vertex set V , then the eccentric connectivity of G, ξ C (G), is defined as v∈V deg(v) ec(v) where deg(v) is the degree of a vertex v and ec(v) is its eccentricity. We obtain an exact lower bound on ξ C (G) in terms of order, and show that this bound is satisfied by the star graph. An asymptotically sharp upper bound is also derived. In addition, for trees of give...

Inequalities provide a way to study topological indices relatively. There are two major classes of topological indices: degree-based and distance-based indices. In this paper we provide a relative study of these classes and derive inequalities between degree-based indices such as Randić connectivity, GA, ABC, and harmonic indices and distance-based indices such as eccentric connectivity, connec...

For a connected graph G, the eccentric connectivity index (ECI) and the first Zagreb eccentricity index of G are defined as ( ) ( ) deg ( ) ( ) i c G i G i v V G ξ G v ε v   and ( 2 1 ) ( ) ( ) i G i v G V E G ε v   , respectively, where deg ( ) G i v is the degree of i v in G and ( ) G i ε v denotes the eccentricity of vertex i v in G. In this paper we compare the eccentric connectivity ...