Let G be a graph. In this paper, we study the eccentric connectivity index, the new version of the second Zagreb index and the forth geometric–arithmetic index.. The basic properties of these novel graph descriptors and some inequalities for them are established.

There is a natural linkage between the molecular structures and the bio-medical and pharmacology characteristics. A topological index can be considered as transformation of chemical structure in to real number and has been used as a predictor parameter. There are certain vertex-degree-based topological indices which has been used extensively in the chemical graph theory but recently no further ...

The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established.

Degree sequence measurements on graphs have attracted a lot of research interest in recent decades. Multiplying the degrees adjacent vertices graph Ω provides multiplicative first Zagreb index graph. In context theory, generalized is defined as product sum αth powers vertex Ω, where α real number such that α≠0 and α≠1. The focus this work extremal for several classes including trees, unicyclic,...

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 ...

In this paper, we present sharp bounds for the Zagreb indices, Harary index and hyperWiener index of graphs with a given matching number, and we also completely determine the extremal graphs. © 2010 Elsevier Ltd. All rights reserved.

By d(v|G) and d_2(v|G) are denoted the number of first and second neighborsof the vertex v of the graph G. The first, second, and third leap Zagreb indicesof G are defined asLM_1(G) = sum_{v in V(G)} d_2(v|G)^2, LM_2(G) = sum_{uv in E(G)} d_2(u|G) d_2(v|G),and LM_3(G) = sum_{v in V(G)} d(v|G) d_2(v|G), respectively. In this paper, we generalizethe results of Naji et al. [Commun. Combin. Optim. ...