We derive sharp lower bounds for the first and the second Zagreb indices (M1 and M2 respectively) for trees and chemical trees with the given number of pendent vertices and find optimal trees. M1 is minimized by a tree with all internal vertices having degree 4, while M2 is minimized by a tree where each “stem” vertex is incident to 3 or 4 pendent vertices and one internal vertex, while the res...

Let G be a simple connected molecular graph with vertex set V(G) and edge set E(G). One important modification of classical Zagreb index, called hyper Zagreb index HM(G) is defined as the sum of squares of the degree sum of the adjacent vertices, that is, sum of the terms 2 [ ( ) ( )] G G d u d v  over all the edges of G, where ( ) G d u denote the degree of the vetex u of G. In this paper, th...

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

A numeric parameter which studies the behaviour, structural, toxicological, experimental, and physicochemical properties of chemical compounds under several graphs’ isomorphism is known as topological index. In 2018, Ali Trinajsti? studied first Zagreb connection index Z ...

The multiplicative sum Zagreb index is defined for a simple graph G as the product of the terms dG(u)+dG(v) over all edges uv∈E(G) , where dG(u) denotes the degree of the vertex u of G . In this paper, we present some lower bounds for the multiplicative sum Zagreb index of several graph operations such as union, join, corona product, composition, direct product, Cartesian product and strong pro...

Applications in chemistry motivated mathematicians to define different topological indices for types of graphs. The Hyper-Zagreb index (HM) is an important tool as it integrates the first and second Zagreb indices. In this paper, we characterize trees unicyclic graphs with four eight greatest HM-value, respectively.

Topological indices are the mathematical tools that correlate the chemical structure with various physical properties, chemical reactivity or biological activity numerically. A topological index is a function having a set of graphs as its domain and a set of real numbers as its range. In QSAR/QSPR study, a prediction about the bioactivity of chemical compounds is made on the basis of physico-ch...

In this paper, the Hyper - Zagreb index of the Cartesian product, composition and corona product of graphs are computed. These corrects some errors in G. H. Shirdel et al.[11].

wiener index is a topological index based on distance between every pair of vertices in agraph g. it was introduced in 1947 by one of the pioneer of this area e.g, harold wiener. inthe present paper, by using a new method introduced by klavžar we compute the wiener andszeged indices of some nanostar dendrimers.

Let [Formula: see text] be a graph. A set [Formula: see text] is a distance k-dominating set of G if for every vertex [Formula: see text], [Formula: see text] for some vertex [Formula: see text], where k is a positive integer. The distance k-domination number [Formula: see text] of G is the minimum cardinality among all distance k-dominating sets of G. The first Zagreb index of G is defined as ...