Topological indices are widely used as mathematical tools to analyze different types of graphs emerged in a broad range of applications. The Hyper-Zagreb index (HM) is an important tool because it integrates the first two Zagreb indices. In this paper, we characterize the trees and unicyclic graphs with the first four and first eight greatest HM-value, respectively.

Let G be a simple graph with the vertex set V(G) and edge set E(G) respectively. The degree of a vertex v in G is the number of vertices in G which are connected to v by an edge and denoted by dG(v). A topological index is a graph invarient which is numerical parameter obtained from a graph which characterize its topology.Thus for two isomorphic graphG and H the value of a particular topologica...

Abstract In this study, we characterize the structure and some topological indices of a class random spider trees (RSTs) such as degree-based Gini index, Hoover generalized Zagreb other associated with these. We obtain exact asymptotic distributions number leaves via probabilistic methods. Moreover, relate model to RSTs that evolves in preferential attachment manner.

topological indices are one of the oldest and most widely used descriptors in quantitative structureproperties relationvhips (qspr). amongst the topological indices used a,s descriptors in qspic., the wienerindex is by far the most popular index. as it has been shown that the wiener index has a strong correlationwith the chemical propenies of the compound.in this study, the relationship between...

We discuss topological transitions during parametric resonance in the gauge sector of electroweak theory. It is shown that the resonance leads to separation of topological indices of the gauge and Higgs fields, resulting in topological transitions of non-sphaleron nature.

Topological indices have been used to modeling biological and chemical properties of molecules in quantitive structure property relationship studies and quantitive structure activity studies. All the degree based topological indices have been defined via classical degree concept. In this paper we define a novel degree concept for a vertex of a simple connected graph: S degree. And also we defin...