scholarly journals Wiener and Hyper–Wiener Indices of Unitary Addition Cayley Graphs

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

scholarly journals Hosoya and Harary Polynomials of Hourglass and Rhombic Benzenoid Systems

2020 ◽  
Vol 2020 ◽  
pp. 1-14
Author(s):  
Zhong-Lin Cheng ◽  
Ashaq Ali ◽  
Haseeb Ahmad ◽  
Asim Naseem ◽  
Maqbool Ahmad Chaudhary
Keyword(s):  
Graph Theory ◽  
Topological Index ◽  
Molecular Descriptor ◽  
Wiener Index ◽  
Vital Role ◽  
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, 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.

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

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
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.

scholarly journals On Computation Degree-Based Topological Descriptors for Planar Octahedron Networks

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.

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

2013 ◽  
Vol 568-569 ◽  
pp. 195-197 ◽  
Author(s):  
Ivan Gutman ◽  
Mohamed Essalih ◽  
Mohamed El Marraki ◽  
Boris Furtula
Keyword(s):  
Graph Theory ◽  
Wiener Index ◽  
Chemical Graph ◽  
Chemical Graph Theory

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

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] .

scholarly journals Revan and hyper-Revan indices of Octahedral and icosahedral networks

2018 ◽  
Vol 3 (1) ◽  
pp. 33-40 ◽  
Author(s):  
Abdul Qudair Baig ◽  
Muhammad Naeem ◽  
Wei Gao
Keyword(s):  
Graph Theory ◽  
Connected Graph ◽  
Vertex Degree ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Vertex Set

AbstractLet G be a connected graph with vertex set V(G) and edge set E(G). Recently, the Revan vertex degree concept is defined in Chemical Graph Theory. The first and second Revan indices of G are defined as R1(G) = $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[rG(u) + rG(v)] and R2(G) = $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[rG(u)rG(v)], where uv means that the vertex u and edge v are adjacent in G. The first and second hyper-Revan indices of G are defined as HR1(G) = $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[rG(u) + rG(v)]2 and HR2(G) = $\begin{array}{} \displaystyle \sum\limits_{uv\in E} \end{array}$[rG(u)rG(v)]2. In this paper, we compute the first and second kind of Revan and hyper-Revan indices for the octahedral and icosahedral networks.

scholarly journals On Sombor Index

Symmetry ◽  
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.

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.

scholarly journals Computing Topological Indices for Para-Line Graphs of Anthracene

2019 ◽  
Vol 17 (1) ◽  
pp. 955-962 ◽  
Author(s):  
Zhiqiang Zhang ◽  
Zeshan Saleem Mufti ◽  
Muhammad Faisal Nadeem ◽  
Zaheer Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
...  
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Line Graph ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Molar Refraction ◽  
Chromatographic Behavior ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
And Mathematics

AbstractAtoms displayed as vertices and bonds can be shown by edges on a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties such as the molar refraction, molar volume, chromatographic behavior, heat of atomization, heat of vaporization, magnetic susceptibility, and the partition coefficient. Today, industry is flourishing because of the interdisciplinary study of different disciplines. This provides a way to understand the application of different disciplines. Chemical graph theory is a mixture of chemistry and mathematics, which plays an important role in chemical graph theory. Chemistry provides a chemical compound, and graph theory transforms this chemical compound into a molecular graphwhich further is studied by different aspects such as topological indices.We will investigate some indices of the line graph of the subdivided graph (para-line graph) of linear-[s] Anthracene and multiple Anthracene.

scholarly journals Eccentricity based topological indices of face centered cubic lattice FCC(n)

2020 ◽  
Vol 44 (1) ◽  
pp. 32-38
Author(s):  
Hani Shaker ◽  
Muhammad Imran ◽  
Wasim Sajjad
Keyword(s):  
Wiener Index ◽  
Face Centered Cubic ◽  
Eccentric Connectivity Index ◽  
Zagreb Index ◽  
Cubic Lattice ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Wide Range ◽  
Unit Cells ◽  
Face Centered

Abstract Chemical graph theory has become a prime gadget for mathematical chemistry due to its wide range of graph theoretical applications for solving molecular problems. A numerical quantity is named as topological index which explains the topological characteristics of a chemical graph. Recently face centered cubic lattice FCC(n) attracted large attention due to its prominent and distinguished properties. Mujahed and Nagy (2016, 2018) calculated the precise expression for Wiener index and hyper-Wiener index on rows of unit cells of FCC(n). In this paper, we present the ECI (eccentric-connectivity index), TCI (total-eccentricity index), CEI (connective eccentric index), and first eccentric Zagreb index of face centered cubic lattice.

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