General Randić, Sum-Connectivity, Hyper-Zagreb and Harmonic Indices, and Harmonic Polynomial of Molecular Graphs

Farahani, Mohammad Reza; Gao, Wei; Kanna, M.R.R.; Kumar, Rajesh; Liu, Jia‐Bao

doi:10.1155/2016/2315949

Cited by 7 publications

(5 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…By applying these tools to the graph of a molecule, researchers can gain insights into its topological properties and predict its behaviour in various chemical or physical contexts. In graph theory, there are topological indices that are associated with graph polynomials and have certain practical applications such as found in the previous studies [21,22]. The study of polynomials discusses the structures of graphs, but they do not always solve the characterization of graph since non-isomorphic graphs appear to have the same polynomial.…”

Section: Introductionmentioning

confidence: 99%

Sombor Index and Sombor Polynomial of the Noncommuting Graph Associated to Some Finite Groups

Sanhan Muhammad Salih Khasraw,

Nor Haniza Sarmin,

Nur Idayu Alimon

et al. 2024

ARASET

View full text Add to dashboard Cite

Sombor index is a newly developed degree-based topological index which involves the degree of the vertex in a simple connected graph. The Sombor index is known as the square root of the sum of the squared degrees of two adjacent vertices in a graph. Meanwhile, the noncommuting graph associated to a group is a graph where its vertices are the non-central elements of the group and two vertices are adjacent if and only if they do not commute. In this study, a new notion called the Sombor polynomial is introduced. Then, the general formula of the Sombor index and the Sombor polynomial of the noncommuting graph associated to some finite groups are determined by using their definitions and some preliminaries. The groups involved in this research are the dihedral groups, the quasidihedral groups, and the generalized quaternion groups. The results found can help the chemists and biologists to predict the chemical and physical properties of the molecules without involving any laboratory work.

show abstract

Section: Introductionmentioning

confidence: 99%

Sombor Index and Sombor Polynomial of the Noncommuting Graph Associated to Some Finite Groups

Sanhan Muhammad Salih Khasraw,

Nor Haniza Sarmin,

Nur Idayu Alimon

et al. 2024

ARASET

View full text Add to dashboard Cite

show abstract

“…In general, they are classified into distance or degree-based topological indices along with these counting related indices of graphs have play a vital role in chemical characterization. Article [6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22] can give more deep insight as literature survey.…”

Section: Introductionmentioning

confidence: 99%

On Vertex-Edge-Degree Topological Descriptors for Certain Crystal Networks

Husain¹,

Abolaban²,

Ahmad³

et al. 2022

Computer Systems Science and Engineering

View full text Add to dashboard Cite

Due to the combinatorial nature of graphs they are used easily in pure sciences and social sciences. The dynamical arrangement of vertices and their associated edges make them flexible (like liquid) to attain the shape of any physical structure or phenomenon easily. In the field of ICT they are used to reflect distributed component and communication among them. Mathematical chemistry is another interesting domain of applied mathematics that endeavors to display the structure of compounds that are formed in result of chemical reactions. This area attracts the researchers due to its applications in theoretical and organic chemistry. It also inspires the mathematicians due to involvement of mathematical structures. Regular or irregular bonding ability of molecules and their formation of chemical compounds can be analyzed using atomic valences (vertex degrees). Pictorial representation of these compounds helps in identifying their properties by computing different graph invariants that is really considered as an application of graph theory. This paper reflects the work on topological indices such as ev-degree Zagreb index, the first ve-degree Zagreb index, the first ve-degree Zagreb index, the second ve-degree Zagreb index, ve-degree Randic index, the ev-degree Randic index, the ve-degree atom-bond connectivity index, the ve-degree geometric-arithmetic index, the ve-degree harmonic index and the ve-degree sum-connectivity index for crystal structural networks namely, bismuth tri-iodide and lead chloride. In this article we have determine the exact values of ve-degree and ev-degree based topological descriptors for crystal networks.

show abstract

“…Since last few years, numerous researchers conducted for the expansion of TD because of their significance [6][7][8][9]. For detail study of TD see [10][11][12][13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Comparative Study of Valency-Based Topological Descriptor for Hexagon Star Network

Koam¹,

Ahmad²,

Nadeem³

2021

Computer Systems Science and Engineering

View full text Add to dashboard Cite

A class of graph invariants referred to today as topological indices are inefficient progressively acknowledged by scientific experts and others to be integral assets in the depiction of structural phenomena. The structure of an interconnection network can be represented by a graph. In the network, vertices represent the processor nodes and edges represent the links between the processor nodes. Graph invariants play a vital feature in graph theory and distinguish the structural properties of graphs and networks. A topological descriptor is a numerical total related to a structure that portray the topology of structure and is invariant under structure automorphism. There are various uses of graph theory in the field of basic science. The main notable utilization of a topological descriptor in science was by Wiener in the investigation of paraffin breaking points. In this paper we study the topological descriptor of a newly design hexagon star network. More preciously, we have computed variation of the Randic 0 R 0 , fourth Zagreb M 4 , fifth Zagreb M 5 , geometric-arithmetic GA; atom-bond connectivity ABC; harmonic H; symmetric division degree SDD; first redefined Zagreb, second redefined Zagreb, third redefined Zagreb, augmented Zagreb AZI, Albertson A; Irregularity measures, Reformulated Zagreb, and forgotten topological descriptors for hexagon star network. In the analysis of the quantitative structure property relationships (QSPRs) and the quantitative structure activity relationships (QSARs), graph invariants are important tools to approximate and predicate the properties of the biological and chemical compounds. We also gave the numerical and graphical representations comparisons of our different results.

show abstract

General Randić, Sum-Connectivity, Hyper-Zagreb and Harmonic Indices, and Harmonic Polynomial of Molecular Graphs

Abstract: We present explicit formula for the general Randić connectivity, general sum-connectivity, Hyper-Zagreb and Harmonic Indices, and Harmonic polynomial of some simple connected molecular graphs.

Cited by 7 publications

References 21 publications

Sombor Index and Sombor Polynomial of the Noncommuting Graph Associated to Some Finite Groups

Sombor Index and Sombor Polynomial of the Noncommuting Graph Associated to Some Finite Groups

On Vertex-Edge-Degree Topological Descriptors for Certain Crystal Networks

Comparative Study of Valency-Based Topological Descriptor for Hexagon Star Network

Contact Info

Product

Resources

About