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 SOME BOUNDS ON SUM CONNECTIVITY AND PRODUCT CONNECTIVITY ZAGREB-K-BANHATTI INDICES OF GRAPHS.

2020 ◽  
Vol 9 (9) ◽  
pp. 144-157
Keyword(s):  
Graph Theory ◽  
Upper Bounds ◽  
Chemical Characteristics ◽  
Lower And Upper Bounds ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Connectivity Indices

The connectivity indices are applied to measure the chemical characteristics of compound in Chemical Graph Theory. In this paper, we introduce the sum connectivity Zagreb-K-Banhatti index and product connectivity Zagreb-K-Banhatti index of a graph. We provide lower and upper bounds for the sum connectivity Zagreb-K-Banhatti index and product connectivity Zagreb-K-Banhatti index of a graph in terms of Zagreb and K-Banhatti indices.

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.

scholarly journals On Realization and Characterization of Topological Indices

2019 ◽  
Vol 9 (1) ◽  
pp. 715-718
Keyword(s):  
Topological Index ◽  
Fixed Number ◽  
Topological Indices ◽  
Molecular Structures ◽  
Real Numbers ◽  
Graph Invariants ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Chemical Graph Theory

In chemical graph theory, topological index is one of the graph invariants which is a fixed number based on structure of a graph. Topological index is used as one of the tool to analyze molecular structures and for proper and optimal design of nanostructure. In this paper we realize the real numbers that are topological indices such as Zagreb indices, Randic index, NK-index, multiplicative F-index and multiplicative Zagreb indices along with some characterizations.

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 On the maximum and minimum first reformulated Zagreb index of graphs with connectivity at most k

Filomat ◽  
2011 ◽  
Vol 25 (4) ◽  
pp. 75-83 ◽  
Author(s):  
Guifu Su ◽  
Liming Xiong ◽  
Lan Xu ◽  
Beibei Ma
Keyword(s):  
Graph Theory ◽  
Extremal Graphs ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Chemical Graph Theory

The authors Milicevic et al. introduced the reformulated Zagreb indices [1], which is a generalization of classical Zagreb indices of chemical graph theory. In this paper, we mainly consider the maximum and minimum for the first reformulated index of graphs with connectivity at most k. The corresponding extremal graphs are characterized.

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

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.

Tetracyclic graphs with maximum second Zagreb index: A simple approach

2018 ◽  
Vol 11 (05) ◽  
pp. 1850064 ◽  
Author(s):  
Akbar Ali
Keyword(s):  
Graph Theory ◽  
Short Note ◽  
Topological Indices ◽  
Simple Approach ◽  
Graph Invariants ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Second Zagreb Index ◽  
Chemical Graph Theory

In the chemical graph theory, graph invariants are usually referred to as topological indices. The second Zagreb index (denoted by [Formula: see text]) is one of the most studied topological indices. For [Formula: see text], let [Formula: see text] be the collection of all non-isomorphic connected graphs with [Formula: see text] vertices and [Formula: see text] edges (such graphs are known as tetracyclic graphs). Recently, Habibi et al. [Extremal tetracyclic graphs with respect to the first and second Zagreb indices, Trans. on Combin. 5(4) (2016) 35–55.] characterized the graph having maximum [Formula: see text] value among all members of the collection [Formula: see text]. In this short note, an alternative but relatively simple approach is used for characterizing the aforementioned graph.

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 On Some Properties of Multiplicative Topological Indices in Silicon-Carbon

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Abid Mahboob ◽  
Sajid Mahboob ◽  
Mohammed M. M. Jaradat ◽  
Nigait Nigar ◽  
Imran Siddique
Keyword(s):  
Graph Theory ◽  
Structural Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Google Maps ◽  
Chemical Graph ◽  
Zagreb Indices ◽  
Silicon Carbon ◽  
Connectivity Indices

The use of graph theory can be visualized in nanochemistry, computer networks, Google maps, and molecular graph which are common areas to elaborate application of this subject. In nanochemistry, a numeric number (topological index) is used to estimate the biological, physical, and structural properties of chemical compounds that are associated with the chemical graph. In this paper, we compute the first and second multiplicative Zagreb indices ( M 1 G and ( M 1 G )), generalized multiplicative geometric arithmetic index ( GA α II G ), and multiplicative sum connectivity and multiplicative product connectivity indices ( SCII G and PCII G ) of SiC 4 − I m , n and SiC 4 − II m , n .

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.

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