A topological index (TI) is a function that associates numeric number to the under-study molecular graph. The first TI based on distance was presented by Wiener find boiling point of paraffins. In 1972, compute total ? -electron energy molecule, degree-based indices are used. this paper, we obtained and second Zagreb con...

For a simple graph G with n vertices and m edges, the inequality M1(G)/n ≤ M2(G)/m, where M1(G) and M2(G) are the first and the second Zagreb indices of G, is known as Zagreb indices inequality. Generalization of these indices gives first M1(G) and second M2(G) variable Zagreb indices. Vukičević in [13] has given an incomplete proof for the claim: for all simple graphs and all λ ∈ [0, 12 ], hol...

The Zagreb indices are among the oldest and the most famous topological molecular structure-descriptors. The first Zagreb index is equal to the sum of the squares of the degrees of the vertices, and the second Zagreb index is equal to the sum of the products of the degrees of pairs of adjacent vertices of the respective graph. In this paper, we characterize the extremal graphs with maximal, sec...

Recently two new degree concepts have been defined in graph theory: ev-degree and ve-degree. Also the evdegree and ve-degree Zagreb and Randić indices have been defined very recently as parallel of the classical definitions of Zagreb and Randić indices. It was shown that ev-degree and ve-degree topological indices can be used as possible tools in QSPR researches . In this paper we d...

Let G = (V,E) be a simple graph with n = |V | vertices and m = |E| edges; let d1, d2, . . . , dn denote the degrees of the vertices of G. If ∆ = max i di ≤ 4, G is a chemical graph. The first and second Zagreb indices are defined as M1 = ∑

The aim of this paper is using the majorization technique to identify the classes of trees with extermal (minimal or maximal) value of some topological indices, among all trees of order n ≥ 12