scholarly journals On correlation of hyperbolic volumes of fullerenes with their properties

2020 ◽  
Vol 8 (1) ◽  
pp. 150-167
Author(s):  
A. A. Egorov ◽  
A Yu. Vesnin
Keyword(s):  
Dimensional Space ◽  
Chemical Properties ◽  
Wiener Index ◽  
Topological Indices ◽  
3 Dimensional ◽  
Hyperbolic Volume ◽  
Chemical Descriptor ◽  
Hyperbolic Polyhedra ◽  
Hyperbolic Volumes ◽  
Initial List

AbstractWe observe that fullerene graphs are one-skeletons of polyhedra, which can be realized with all dihedral angles equal to π /2 in a hyperbolic 3-dimensional space. One of the most important invariants of such a polyhedron is its volume. We are referring this volume as a hyperbolic volume of a fullerene. It is known that some topological indices of graphs of chemical compounds serve as strong descriptors and correlate with chemical properties. We demonstrate that hyperbolic volume of fullerenes correlates with few important topological indices and so, hyperbolic volume can serve as a chemical descriptor too. The correlation between hyperbolic volume of fullerene and its Wiener index suggested few conjectures on volumes of hyperbolic polyhedra. These conjectures are confirmed for the initial list of fullerenes.

ON THE WIENER INDEX OF F_H SUMS OF GRAPHS

2021 ◽  
Vol 3 (2) ◽  
pp. 37-57
Author(s):  
L. Alex ◽  
Indulal G
Keyword(s):  
Complete Graph ◽  
Cartesian Product ◽  
Chemical Properties ◽  
Wiener Index ◽  
Topological Indices ◽  
Single Vertex ◽  
Molecular Graphs ◽  
New Class ◽  
And Chemical Properties

Wiener index is the first among the long list of topological indices which was used to correlate structural and chemical properties of molecular graphs. In \cite{Eli} M. Eliasi, B. Taeri defined four new sums of graphs based on the subdivision of edges with regard to the cartesian product and computed their Wiener index. In this paper, we define a new class of sums called $F_H$ sums and compute the Wiener index of the resulting graph in terms of the Wiener indices of the component graphs so that the results in \cite{Eli} becomes a particular case of the Wiener index of $F_H$ sums for $H = K_1$, the complete graph on a single vertex.

Topological Characterization of the Third Type of Triangular Hex-derived Networks

2021 ◽  
Vol 31 (2) ◽  
pp. 145-161
Author(s):  
Shibsankar Das ◽  
◽  
Shikha Rai ◽  
Keyword(s):  
Chemical Structure ◽  
Recent Literature ◽  
Chemical Properties ◽  
Topological Indices ◽  
Topological Characterization ◽  
The Third ◽  
Chemical Descriptor ◽  
Different Dimensions ◽  
And Chemical Properties

A topological index is a numerical quantity that defines a chemical descriptor to report several physical, biological and chemical properties of a chemical structure. In recent literature, various degree-based topological indices of a molecular structure are easily calculated by deriving a M-polynomial of that structure. In this paper, we first determine the expression of a M-polynomial of the triangular Hex-derived network of type three of dimension n and then obtain the corresponding degree-based topological indices from the closed form of M-polynomial. In addition, we use Maple software to represent the M-polynomial and the concerned degree-based topological indices pictorially for different dimensions.

scholarly journals On the Degree-Based Topological Indices of Some Derived Networks

Mathematics ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 612 ◽  
Author(s):  
Haidar Ali ◽  
Muhammad Ahsan Binyamin ◽  
Muhammad Kashif Shafiq ◽  
Wei Gao
Keyword(s):  
Chemical Structure ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Topological Indices ◽  
Theoretical Chemistry ◽  
Zagreb Index ◽  
Entire Structure ◽  
Physical Chemical ◽  
Chemical Descriptors

There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randić index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, A B C 4 index, and G A 5 index for the third type of hex-derived networks theoretically.

scholarly journals The Wiener and Zagreb Indices of Conjugacy Class Graph of the Dihedral Groups

MATEMATIKA ◽  
2019 ◽  
Vol 35 (1) ◽  
pp. 51-57 ◽  
Author(s):  
Nur Idayu Alimon ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Conjugacy Class ◽  
Chemical Properties ◽  
Wiener Index ◽  
Topological Indices ◽  
Dihedral Groups ◽  
Zagreb Index ◽  
Vertex Set ◽  
Class Graph ◽  
The First Zagreb Index ◽  
Group Of Symmetries

Topological indices are numerical values that can be analysed to predict the chemical properties of the molecular structure and the topological indices are computed for a graph related to groups. Meanwhile, the conjugacy class graph of  is defined as a graph with a vertex set represented by the non-central conjugacy classes of . Two distinct vertices are connected if they have a common prime divisor. The main objective of this article is to find various topological indices including the Wiener index, the first Zagreb index and the second Zagreb index for the conjugacy class graph of dihedral groups of order  where the dihedral group is the group of symmetries of regular polygon, which includes rotations and reflections. Many topological indices have been determined for simple and connected graphs in general but not graphs related to groups.  In this article, the Wiener index and Zagreb index of conjugacy class graph of dihedral groups are generalized.

scholarly journals Weighted Wiener Indices of Molecular Graphs with Application to Alkenes and Alkadienes

Mathematics ◽  
2021 ◽  
Vol 9 (2) ◽  
pp. 153
Author(s):  
Simon Brezovnik ◽  
Niko Tratnik ◽  
Petra Žigert Pleteršek
Keyword(s):  
Linear Regression Analysis ◽  
Chemical Properties ◽  
Wiener Index ◽  
Topological Indices ◽  
The Other ◽  
Multiple Bonds ◽  
Saturated Hydrocarbons ◽  
Simple Graphs ◽  
Boiling Points ◽  
Physico Chemical

There exist many topological indices that are calculated on saturated hydrocarbons since they can be easily modelled by simple graphs. On the other hand, it is more challenging to investigate topological indices for hydrocarbons with multiple bonds. The purpose of this paper is to introduce a simple model that gives good results for predicting physico-chemical properties of alkenes and alkadienes. In particular, we are interested in predicting boiling points of these molecules by using the well known Wiener index and its weighted versions. By performing the non-linear regression analysis we predict boiling points of alkenes and alkadienes.

Association algorithm with bearing-only measurements in 3-dimensional space

2009 ◽  
Author(s):  
Xiu Jianjuan ◽  
Li Yuli ◽  
He You ◽  
Wang Guohong
Keyword(s):  
Dimensional Space ◽  
3 Dimensional ◽  
Association Algorithm

scholarly journals M-polynomial and topological indices of zigzag edge coronoid fused by starphene

2020 ◽  
Vol 18 (1) ◽  
pp. 1362-1369
Author(s):  
Farkhanda Afzal ◽  
Sabir Hussain ◽  
Deeba Afzal ◽  
Saira Hameed
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Zigzag Edge ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Chemical Graphs

AbstractChemical graph theory is a subfield of graph theory that studies the topological indices for chemical graphs that have a good correlation with chemical properties of a chemical molecule. In this study, we have computed M-polynomial of zigzag edge coronoid fused by starphene. We also investigate various topological indices related to this graph by using their M-polynomial.

Triharmonic Riemannian submersions from 3-dimensional space forms

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Tomoya Miura ◽  
Shun Maeta
Keyword(s):  
Existence Theorem ◽  
Space Form ◽  
Dimensional Space ◽  
Riemannian Submersion ◽  
Partial Answer ◽  
Riemannian Submersions ◽  
Space Forms ◽  
3 Dimensional

Abstract We show that any triharmonic Riemannian submersion from a 3-dimensional space form into a surface is harmonic. This is an affirmative partial answer to the submersion version of the generalized Chen conjecture. Moreover, a non-existence theorem for f -biharmonic Riemannian submersions is also presented.

scholarly journals Topological Indices of Para-line Graphs of V-Phenylenic Nanostructures

2019 ◽  
Vol 17 (1) ◽  
pp. 260-266 ◽  
Author(s):  
Imran Nadeem ◽  
Hani Shaker ◽  
Muhammad Hussain ◽  
Asim Naseem
Keyword(s):  
Chemical Properties ◽  
Topological Indices ◽  
Structural Chemistry ◽  
Line Graphs ◽  
Physical And Chemical Properties ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Physical And Chemical ◽  
And Chemical Properties

Abstract The degree-based topological indices are numerical graph invariants which are used to correlate the physical and chemical properties of a molecule with its structure. Para-line graphs are used to represent the structures of molecules in another way and these representations are important in structural chemistry. In this article, we study certain well-known degree-based topological indices for the para-line graphs of V-Phenylenic 2D lattice, V-Phenylenic nanotube and nanotorus by using the symmetries of their molecular graphs.

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