Hosoya and Harary Polynomials of Hourglass and Rhombic Benzenoid Systems

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Harry Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we compute the Hosoya polynomials for hourglass and rhombic benzenoid systems and recover Wiener and hyper-Wiener indices from them.

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Hosoya and Harary Polynomials of TOX(n),RTOX(n),TSL(n) and RTSL(n)

Discrete Dynamics in Nature and Society ◽

10.1155/2019/8696982 ◽

2019 ◽

Vol 2019 ◽

pp. 1-18 ◽

Cited By ~ 1

Author(s):

Lian Chen ◽

Abid Mehboob ◽

Haseeb Ahmad ◽

Waqas Nazeer ◽

Muhammad Hussain ◽

...

Keyword(s):

Topological Index ◽

Molecular Descriptor ◽

Wiener Index ◽

Vital Role ◽

Harary Index ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Hosoya Polynomial ◽

Molecular Branching ◽

Path Number

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we computed the Hosoya and the Harary polynomials for TOX(n),RTOX(n),TSL(n), and RTSL(n) networks. Moreover, we computed serval distance based topological indices, for example, Wiener index, Harary index, and multiplicative version of wiener index.

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Wiener and Hyper–Wiener Indices of Unitary Addition Cayley Graphs

International Journal of Recent Technology and Engineering - 2 ◽

10.35940/ijrte.b1022.0782s319 ◽

2019 ◽

Vol 8 (2S3) ◽

pp. 131-132

Keyword(s):

Graph Theory ◽

Cayley Graph ◽

Topological Index ◽

Cayley Graphs ◽

Wiener Index ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Shortest Distance ◽

Vertex Set

A topological index is a number associated to a graph. In chemical graph theory the Wiener index of a graph G, denoted by W(G) is the sum of the distance between all (unordered) pairs of vertices of G. That is, W(G) = ,where d (ui , uj) is the shortest distance between the vertices. ui and uj .The Hyper-Wiener Index WW(G) is the generalization of the Wiener index. The Hyper- Wiener Index of a graph G is, WW (G) = .The unitary addition Cayley graph Gn has a vertex set Zn = {0, 1,…, n-1} and the vertices u and v are adjacent if gcd (u+v,n) =1. In this paper Wiener index and Hyper Wiener indices of Unitary addition Cayley graph Gn is computed

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On Computation Degree-Based Topological Descriptors for Planar Octahedron Networks

Journal of Mathematics ◽

10.1155/2021/4880092 ◽

2021 ◽

Vol 2021 ◽

pp. 1-12

Author(s):

Wang Zhen ◽

Parvez Ali ◽

Haidar Ali ◽

Ghulam Dustigeer ◽

Jia-Bao Liu

Keyword(s):

Graph Theory ◽

Chemical Compound ◽

Topological Index ◽

Molecular Graph ◽

Topological Descriptors ◽

Zagreb Index ◽

Chemical Graph ◽

Symmetric Division ◽

Chemical Graph Theory ◽

Augmented Zagreb Index

A molecular graph is used to represent a chemical molecule in chemical graph theory, which is a branch of graph theory. A graph is considered to be linked if there is at least one link between its vertices. A topological index is a number that describes a graph’s topology. Cheminformatics is a relatively young discipline that brings together the field of sciences. Cheminformatics helps in establishing QSAR and QSPR models to find the characteristics of the chemical compound. We compute the first and second modified K-Banhatti indices, harmonic K-Banhatti index, symmetric division index, augmented Zagreb index, and inverse sum index and also provide the numerical results.

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M-Polynomials and Degree-Based Topological Indices of Triangular, Hourglass, and Jagged-Rectangle Benzenoid Systems

Journal of Chemistry ◽

10.1155/2018/8213950 ◽

2018 ◽

Vol 2018 ◽

pp. 1-8 ◽

Cited By ~ 8

Author(s):

Young Chel Kwun ◽

Ashaq Ali ◽

Waqas Nazeer ◽

Maqbool Ahmad Chaudhary ◽

Shin Min Kang

Keyword(s):

Graph Theory ◽

Biological Properties ◽

Vital Role ◽

Topological Indices ◽

Molecular Topology ◽

Chemical Graph ◽

Chemical Structures ◽

Research Fields ◽

Chemical Graph Theory ◽

Active Research

Chemical graph theory is a branch of mathematical chemistry which has an important effect on the development of the chemical sciences. The study of topological indices is currently one of the most active research fields in chemical graph theory. Topological indices help to predict many chemical and biological properties of chemical structures under study. The aim of this report is to study the molecular topology of some benzenoid systems. M-polynomial has wealth of information about the degree-based topological indices. We compute M-polynomials for triangular, hourglass, and jagged-rectangle benzenoid systems, and from these M-polynomials, we recover nine degree-based topological indices. Our results play a vital role in pharmacy, drug design, and many other applied areas.

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Why plerograms are not used in chemical graph theory? The case of terminal-Wiener index

Chemical Physics Letters ◽

10.1016/j.cplett.2013.03.045 ◽

2013 ◽

Vol 568-569 ◽

pp. 195-197 ◽

Cited By ~ 2

Author(s):

Ivan Gutman ◽

Mohamed Essalih ◽

Mohamed El Marraki ◽

Boris Furtula

Keyword(s):

Graph Theory ◽

Wiener Index ◽

Chemical Graph ◽

Chemical Graph Theory

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Banhatti, revan and hyper-indices of silicon carbide Si2C3-III[n,m]

Open Chemistry ◽

10.1515/chem-2020-0151 ◽

2021 ◽

Vol 19 (1) ◽

pp. 646-652

Author(s):

Dongming Zhao ◽

Manzoor Ahmad Zahid ◽

Rida Irfan ◽

Misbah Arshad ◽

Asfand Fahad ◽

...

Keyword(s):

Silicon Carbide ◽

Graph Theory ◽

Topological Index ◽

Molecular Graph ◽

Graphical Analysis ◽

Topological Indices ◽

Chemical Bonds ◽

Chemical Graph ◽

Molecular Graphs ◽

Chemical Graph Theory

Abstract In recent years, several structure-based properties of the molecular graphs are understood through the chemical graph theory. The molecular graph G G of a molecule consists of vertices and edges, where vertices represent the atoms in a molecule and edges represent the chemical bonds between these atoms. A numerical quantity that gives information related to the topology of the molecular graphs is called a topological index. Several topological indices, contributing to chemical graph theory, have been defined and vastly studied. Recent inclusions in the class of the topological indices are the K-Banhatti indices. In this paper, we established the precise formulas for the first and second K-Banhatti, modified K-Banhatti, K-hyper Banhatti, and hyper Revan indices of silicon carbide Si 2 C 3 {{\rm{Si}}}_{2}{{\rm{C}}}_{3} - III [ n , m ] {\rm{III}}\left[n,m] . In addition, we present the graphical analysis along with the comparison of these indices for Si 2 C 3 {{\rm{Si}}}_{2}{{\rm{C}}}_{3} - III [ n , m ] {\rm{III}}\left[n,m] .

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Topology-Based Analysis of OTIS (Swapped) Networks OKn and OPn

Journal of Chemistry ◽

10.1155/2019/4291943 ◽

2019 ◽

Vol 2019 ◽

pp. 1-11

Author(s):

Hai-Xia Li ◽

Sarfaraz Ahmad ◽

Iftikhar Ahmad

Keyword(s):

Topological Index ◽

Molecular Descriptor ◽

Randić Index ◽

Zagreb Index ◽

Randic Index ◽

Chemical Graph ◽

Zagreb Indices ◽

Second Zagreb Index ◽

Chemical Graph Theory ◽

Augmented Zagreb Index

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In this paper, M-polynomial OKn and OPn networks are computed. The M-polynomial is rich in information about degree-based topological indices. By applying the basic rules of calculus on M-polynomials, the first and second Zagreb indices, modified second Zagreb index, general Randić index, inverse Randić index, symmetric division index, harmonic index, inverse sum index, and augmented Zagreb index are recovered.

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Multiplicative topological indices of honeycomb derived networks

Open Physics ◽

10.1515/phys-2019-0003 ◽

2019 ◽

Vol 17 (1) ◽

pp. 16-30

Author(s):

Jiang-Hua Tang ◽

Mustafa Habib ◽

Muhammad Younas ◽

Muhammad Yousaf ◽

Waqas Nazeer

Keyword(s):

Graph Theory ◽

Structural Properties ◽

Chemical Properties ◽

Vital Role ◽

Topological Indices ◽

Chemical Graph ◽

Chemical Structures ◽

Chemical Graph Theory ◽

Physico Chemical

Abstract Topological indices are the numerical values associated with chemical structures that correlate physico-chemical properties with structural properties. There are various classes of topological indices such as degree based topological indices, distance based topological indices and counting related topological indices. Among these classes, degree based topological indices are of great importance and play a vital role in chemical graph theory, particularly in chemistry. In this report, we have computed the multiplicative degree based topological indices of honeycomb derived networks of dimensions I, 2, 3 and 4.

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On Sombor Index

Symmetry ◽

10.3390/sym13010140 ◽

2021 ◽

Vol 13 (1) ◽

pp. 140

Author(s):

Kinkar Chandra Das ◽

Ahmet Sinan Çevik ◽

Ismail Naci Cangul ◽

Yilun Shang

Keyword(s):

Graph Theory ◽

Topological Index ◽

Upper Bounds ◽

Lower And Upper Bounds ◽

Chemical Graph ◽

Zagreb Indices ◽

Chemical Graph Theory ◽

Degree Of Vertex ◽

Graph Parameters ◽

Future Work

The concept of Sombor index (SO) was recently introduced by Gutman in the chemical graph theory. It is a vertex-degree-based topological index and is denoted by Sombor index SO: SO=SO(G)=∑vivj∈E(G)dG(vi)2+dG(vj)2, where dG(vi) is the degree of vertex vi in G. Here, we present novel lower and upper bounds on the Sombor index of graphs by using some graph parameters. Moreover, we obtain several relations on Sombor index with the first and second Zagreb indices of graphs. Finally, we give some conclusions and propose future work.

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

Open Chemistry ◽

10.1515/chem-2020-0161 ◽

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.

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