we give sharp upper bounds on the zagreb indices and lower bounds on the zagreb coindices of chemical trees and characterize the case of equality for each of these topological invariants.

Let G be a connected graph. The multiplicative Zagreb eccentricity indices of G are defined respectively as Π1(G) = ∏ v∈V (G) ε 2 G(v) and Π ∗ 2(G) = ∏ uv∈E(G) εG(u)εG(v), where εG(v) is the eccentricity of vertex v in graph G and εG(v) = (εG(v)) . In this paper, we present some bounds of the multiplicative Zagreb eccentricity indices of Cartesian product graphs by means of some invariants of t...

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zag...

Let G be a graph. The first Zagreb M1(G) of graph G is defined as: M1(G) = uV(G) deg(u)2. In this paper, we prove that each even number except 4 and 8 is a first Zagreb index of a caterpillar. Also, we show that the fist Zagreb index cannot be an odd number. Moreover, we obtain the fist Zagreb index of some graph operations.

in this paper we give sharp upper bounds on the zagreb indices and characterize all trees achieving equality in these bounds. also, we give lower bound on first zagreb coindex of trees.