The forgotten topological coindex (also called Lanzhou index) is defined for a simple connected graph G as the sum of the terms du2+dv2 over all non-adjacent vertex pairs uv of G, where du denotes the degree of the vertex u in G. In this paper, we present some inequalit...

the mathematical properties of nano molecules are an interesting branch of nanoscience forresearches nowadays. the periodic open single wall tubulene is one of the nano moleculeswhich is built up from two caps and a distancing nanotube/neck. we discuss how toautomatically construct the graph of this molecule and plot the graph by spring layoutalgorithm in graphviz and netwrokx packages. the sim...

The first reformulated Zagreb index $EM_1(G)$ of a simple graph $G$ is defined as the sum of the terms $(d_u+d_v-2)^2$ over all edges $uv$ of $G .$ In this paper, the various upper and lower bounds for the first reformulated Zagreb index of a connected graph interms of other topological indices are obtained.

Graph theory has provided a very useful tool, called topological indices which are a number obtained from the graph $G$ with the property that every graph $H$ isomorphic to $G$, value of a topological index must be same for both $G$ and $H$. In this article, we present exact expressions for some topological indices of k-th subdivision graph and semi total point graphs respectively, which are a ...

The Hosoya index of a graph is defined as the total number of the matchings, including the empty edge set, of the graph. The Merrifield-Simmons index of a graph is defined as the total number of the independent vertex sets, including the empty vertex set, of the graph. Let U(n,∆) be the set of connected unicyclic graphs of order n with maximum degree ∆. We consider the Hosoya indices and the Me...

the edge detour index polynomials were recently introduced for computing theedge detour indices. in this paper we nd relations among edge detour polynomials for the2-dimensional graph of tuc4c8(s) in a euclidean plane and tuc4c8(s) nanotorus.

In theoretical chemistry, the researchers use graph models to express the structure of molecular, and the Zagreb indices and multiplicative Zagreb indices defined on molecular graph G are applied to measure the chemical characteristics of compounds and drugs. In this paper, we present the exact expressions of multiplicative Zagreb indices for certain important chemical structures like nanotube,...

Abstract In this paper, the exact formulae for the Harary indices of join, disjunction, symmetric difference, strong product of graphs are obtained. Also, the Schultz and modified Schultz indices of join and strong product of graphs are computed. We apply some of our results to compute the Harary, Schultz and modified Schultz indices of fan graph, wheel graph, open fence and closed fence graphs.