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. ...

Triazine-based covalent organic frameworks (TriCFs) were synthesized using melamine, and cyanuric acid is a brand-new synthetic lubricant, which thermo-stable possesses lamellar structure. This article demonstrates how topological descriptors for the TriCF structure are precisely evaluated degree sum of end vertex neighbors also some molecular with multiplicative neighborhood sums evaluated. Fu...

In this note, we give expressions for the first(second) Zagreb coindex, second Zagreb index(coindex), third Zagreb index and first hyper-Zagreb index of the line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p, q] and obtain upper bounds for Wiener index and degree-distance index of these graphs. This note continue the program of computing certain topological indi...

The atom-bond connectivity (ABC) index is a degree-based graph topological index that found chemical applications. The problem of complete characterization of trees with minimal ABC index is still an open problem. In [14], it was shown that trees with minimal ABC index do not contain so-called Bk-branches, with k ≥ 5, and that they do not have more than four B4-branches. Our main results here r...

‎the harmonic index of a connected graph $g$‎, ‎denoted by $h(g)$‎, ‎is‎ ‎defined as $h(g)=sum_{uvin e(g)}frac{2}{d_u+d_v}$‎ ‎where $d_v$ is the degree of a vertex $v$ in g‎. ‎in this paper‎, ‎expressions for the harary indices of the‎ ‎join‎, ‎corona product‎, ‎cartesian product‎, ‎composition and symmetric difference of graphs are‎ ‎derived‎.

The forgotten topological index is defined as sum of third power of degrees. In this paper, we compute some properties of forgotten index and then we determine it for some classes of product graphs.

The eccentric connectivity index ξ is a distance–based molecular structure descriptor that was recently used for mathematical modeling of biological activities of diverse nature. We prove that the broom has maximum ξ among trees with a fixed maximum vertex degree, and characterize such trees with minimum ξ . In addition, we propose a simple linear algorithm for calculating ξ of trees.

This paper proposes a concept of uncertain random graph in which some edges exist with some degrees in probability measure and others exist with some degrees in uncertain measure, and discusses the connectivity index of an uncertain random graph. In addition, this paper presents a concept uncertain random network in which some weights are random variables and others are uncertain variables, and...

Motivation. The Randiü index is one of the most successful molecular descriptors in structure–property and structure–activity relationships studies. In spite of some attempts to interpret the physical meaning of this index it is still not clear what exactly this index measures in a molecular structure. The finding of the structural interpretation of this topological index will open the doors to...