In a study on the structure–dependency of the total π-electron energy from 1972, Trinajstić and one of the present authors have shown that it depends on the sums ∑ v∈V d(v) 2 and ∑ v∈V d(v) , where d(v) is the degree of a vertex v of the underling molecular graph G. The first sum was later named first Zagreb index and over the years became one of the most investigated graph–based molecular stru...

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.

Abstract A topological descriptor is a mathematical illustration of molecular construction that relates particular physicochemical properties primary structure as well its depiction. Topological co-indices are usually applied for quantitative actions relationships (QSAR) and structures property (QSPR). descriptors which considered the noncontiguous vertex set. We study accompanying some renowne...

A topological index is a function having set of graphs as its domain and real numbers range. Here we concentrated on indices involving the number vertices, edges maximum minimum vertex degree. The aim this paper to compute lower upper bounds second Zagreb index, third Hyper Harmonic Redefined first First reformulated Forgotten square F-index, Sum-connectivity Randic Reciprocal Gourava Sombar Ni...

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

Abstract. For a (molecular) graph G with vertex set V (G) and edge set E(G), the first and second Zagreb indices of G are defined as M1(G) = ∑ v∈V (G) dG(v) 2 and M2(G) = ∑ uv∈E(G) dG(u)dG(v), respectively, where dG(v) is the degree of vertex v in G. The alternative expression of M1(G) is ∑ uv∈E(G)(dG(u) + dG(v)). Recently Ashrafi, Došlić and Hamzeh introduced two related graphical invariants M...

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,...

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.

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.