Wiener index is a topological index based on distance between every pair of vertices in a graph G. It was introduced in 1947 by one of the pioneer of this area e.g, Harold Wiener. In the present paper, by using a new method introduced by klavžar we compute the Wiener and Szeged indices of some nanostar dendrimers.

Abstract. Topological indices are the numerical value associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity or biological activity. Graph theory is a delightful playground for the exploration of proof techniques in Discrete Mathematics and its results have applications in many areas of sciences. A graph is a ...

Quantifying the success of the topographic preservation achieved with a neural map is difficult. In this paper we present Topological Correlation, Tc, a method that assesses the degree of topographic preservation achieved based on the linear correlation between the topological distances in the neural map, and the topological distances in the induced Delaunay triangulation of the network nodes. ...

Many existing degree based topological indices can be clasified as bond incident degree (BID) indices, whose general form is BID(G) = ∑ uv∈E(G) Ψ(du, dv), where uv is the edge connecting the vertices u, v of the graph G, E(G) is the edge set of G, du is the degree of the vertex u and Ψ is a non-negative real valued (symmetric) function of du and dv. Here, it has been proven that if the extensio...

A topological index is a real number obtained from the chemical graph structure. It helpful to calculate physicochemical and biological properties of numerous drugs. This done through degree-based indices. In this paper, acarbose, tolazamide, miglitol, prandin, metformin, so on used treat diabetes are discussed, purpose QSPR study determine mathematical relation between under investigation (e.g...

The first and second Zagreb indices of a graph are equal, respectively, to the sum of squares of the vertex degrees, and the sum of the products of the degrees of pairs of adjacent vertices. We now consider analogous graph invariants, based on the second degrees of vertices (number of their second neighbors), called leap Zagreb indices. A number of their basic properties is established.

The atom–bond connectivity index of a graph G is defined as

A recently published paper [T. Došlić, this journal 3 (2012) 25-34] considers the Zagreb indices of benzenoid systems, and points out their low discriminativity. We show that analogous results hold for a variety of vertex-degree-based molecular structure descriptors that are being studied in contemporary mathematical chemistry. We also show that these results are straightforwardly obtained by u...

zagreb indices belong to better known and better researched topological indices. weinvestigate here their ability to discriminate among benzenoid graphs and arrive at some quiteunexpected conclusions. along the way we establish tight (and sometimes sharp) lower andupper bounds on various classes of benzenoids.

This paper explores the method of assessing regional spatial ventilation performance for the design of residential building arrangements at an operational level. Three ventilation efficiency (VE) indices, Net Escape Velocity (NEV), Visitation Frequency (VF) and spatial-mean Velocity Magnitude (VM), are adopted to quantify the influence of design variation on VE within different regional spaces....