We obtain inequalities involving many topological indices in classical graph products by using the f-polynomial. In particular, we work with lexicographic product, Cartesian sum and first Zagreb, forgotten, inverse degree lordeg indices.

In this paper, the weighted Szeged indices of Cartesian product and Corona product of two connected graphs are obtained. Using the results obtained here, the weighted Szeged indices of the hypercube of dimension n, Hamming graph, C4 nanotubes, nanotorus, grid, t−fold bristled, sunlet, fan, wheel, bottleneck graphs and some classes of bridge graphs are computed.

The edge-Wiener index of a connected graph is the sum of the distances between all pairs of edges of the graph. In this paper, we determine the polyphenyl chains with minimum and maximum edge-Wiener indices among all the polyphenyl chains with h hexagons. Moreover, explicit formulas for the edge-Wiener indices of extremal polyphenyl chains are obtained.

The Wiener index of a connected graph is the sum of all pairwise distances of vertices of the graph. In this paper, we consider the Wiener indices of trees with perfect matchings, characterizing the eight trees with smallest Wiener indices among all trees of order 2 ( 11) m m with perfect matchings.

One of the more exciting polynomials among newly presented graph algebraic is M−Polynomial, which a standard method for calculating degree−based topological indices. In this paper, we define Mve−polynomials based on vertex edge degree and derive various vertex–edge indices from them. Thus, any graph, provide some relationships between Also, discuss general Mve−polynomial r−regular simple graph....

let $g=(v,e)$ be a‎ ‎simple graph of order $n$ and size $m$‎. ‎an $r$-matching of $g$ is ‎a set of $r$ edges of $g$ which no two of them have common vertex‎. ‎the hosoya index $z(g)$ of a graph $g$ is defined as the total‎ ‎number of its matchings‎. ‎an independent set of $g$ is a set of‎ ‎vertices where no two vertices are adjacent‎. ‎the ‎merrifield-simmons index of $g$ is defined as the tota...

In past years, topological indices are introduced to measure the characters of chemical molecules. Thus, the study of these topological indices has raised large attention in the field of chemical science, biology science and pharmaceutical science. In this paper, by virtue of molecular structure analysis, we determine the total Szeged index, vertex-edge Wiener index and edge hyper-Wiener index ...

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...

A QSPR study of six sets of partition coefficients of a class of halogenated organic compounds has been performed with the aim to describe the six sets of partition coefficients with a common molecular connectivity descriptor, whose basic parameters can be derived by the aid of the three graph concepts: graph, pseudograph and complete graph. A simple odd complete graph conjecture gives rise to ...

The rst Zagreb index of a graph is equal to the sum of the square of the vertex degrees of the graph and the forgotten topological index (Findex) of a graph is de ned as the sum of cubes of the vertex degrees of the graph. These parameters have applications in chemistry and drug structures. For any xed integer d ≥ 2, the d-ary tree is a rooted tree in which each node has no more than d children...