scholarly journals On F-Polynomial, Multiple and Hyper F-Index of some Molecular Graphs

2018 ◽  
Vol 20 ◽  
pp. 36-43 ◽  
Author(s):  
Sirous Ghobadi ◽  
Mobina Ghorbaninejad
Keyword(s):  
Topological Index ◽  
Graph Automorphism ◽  
Molecular Graphs

A graph can be recognized by a numeric number, a polynomial, a sequence of numbers or a matrix which represent the whole graph, and these representations are aimed to be uniquely defined for that graph. Topological index is a numeric quantity with a graph which characterizes the topology of the graph and is invariant under graph automorphism. In this paper, we compute F-polynomial, Multiple F-index and Hyper F-index for some special graphs.

Computing Analysis of Degree and Connection Based Irregular Indices of Polycyclic Aromatic Hydrocarbons

2021 ◽  
Vol 18 ◽  
Author(s):  
Muhammad Javaid ◽  
Muhammad Ibraheem ◽  
Abdul Raheem
Keyword(s):  
Polycyclic Aromatic Hydrocarbons ◽  
Aromatic Hydrocarbons ◽  
Topological Index ◽  
Medical Science ◽  
Molecular Graph ◽  
Chemical Compounds ◽  
Molecular Graphs ◽  
Equal Degree ◽  
Physical Chemical ◽  
Polycyclic Aromatic

Introduction: A graph is supposed to be regular if all vertices have equal degree, otherwise irregular. Materials and Methods: Polycyclic aromatic hydrocarbons are important combusting material and considered as class of carcinogens. These polycyclic aromatic hydrocarbons play an important role in graphitisation of medical science. A topological index is a function that assigns a numerical value to a (molecular) graph which predicts various physical, chemical, biological, thermodynamical and structural properties of (molecular) graphs. An irregular index is a topological index that measures the irregularity of atoms with respect to their bonding for the chemical compounds which are involved in the under studying graphs. Results and Discussion: In this paper, we will compute an analysis of distance based irregular indices of polycyclic aromatic hydrocarbons. A comparison among the obtained indices with the help of their numerical values and the 3D presentations is also included. The efficient and steady indices of polycyclic aromatic hydrocarbons are addressed in the form of their irregularities. Conclusion: Connection based study of the molecular graphs is more suitable than the degree based irregularity indices.

On Wiener and terminal Wiener index of graphs

2015 ◽  
Vol 08 (05) ◽  
pp. 1550066 ◽  
Author(s):  
J. Baskar Babujee ◽  
J. Senbagamalar
Keyword(s):  
Topological Index ◽  
Wiener Index ◽  
Molecular Graphs ◽  
Structural Descriptor ◽  
Vertex Degrees ◽  
Pendent Vertices ◽  
Sum Of Distances

The Wiener index is a topological index defined as the sum of distances between all pairs of vertices in a graph. It was introduced as a structural descriptor for molecular graphs of alkanes, which are trees with vertex degrees of four at the most. The terminal Wiener index is defined as the sum of distances between all pairs of pendent vertices in a graph. In this paper we investigate Wiener and terminal Wiener for graphs derived from certain operations.

scholarly journals On Knowledge Discovery and Representations of Molecular Structures Using Topological Indices

2021 ◽  
Vol 11 (1) ◽  
pp. 21-32
Author(s):  
Fawaz E. Alsaadi ◽  
Syed Ahtsham Ul Haq Bokhary ◽  
Aqsa Shah ◽  
Usman Ali ◽  
Jinde Cao ◽  
...  
Keyword(s):  
Topological Index ◽  
Chemical Compounds ◽  
Quantitative Structure Activity Relationship ◽  
Topological Indices ◽  
Molecular Structures ◽  
Quantitative Structure ◽  
Structure Property ◽  
Graph Automorphism ◽  
Structure Property Relationship ◽  
Atom Bond

AbstractThe main purpose of a topological index is to encode a chemical structure by a number. A topological index is a graph invariant, which decribes the topology of the graph and remains constant under a graph automorphism. Topological indices play a wide role in the study of QSAR (quantitative structure-activity relationship) and QSPR (quantitative structure-property relationship). Topological indices are implemented to judge the bioactivity of chemical compounds. In this article, we compute the ABC (atom-bond connectivity); ABC4 (fourth version of ABC), GA (geometric arithmetic) and GA5 (fifth version of GA) indices of some networks sheet. These networks include: octonano window sheet; equilateral triangular tetra sheet; rectangular sheet; and rectangular tetra sheet networks.

scholarly journals Total π Electron Energy of Linear Acenes Nanostructure

2016 ◽  
Vol 64 ◽  
pp. 110-115
Author(s):  
Ali Asghar Khakpoor
Keyword(s):  
Electronic Properties ◽  
Electron Energy ◽  
Small Groups ◽  
Topological Index ◽  
Organic Molecules ◽  
Topological Indices ◽  
Special Importance ◽  
Chemical Formula ◽  
Molecular Graphs ◽  
The Family

Moletronics is a branch of nanoelectronic that considers the use of small groups of molecules in nanoscale. A family of organic molecules that has been highly regarded in Moletronics and nanoscale are Acenes with the chemical formula C4n+2H2n+4. Since the identification and analysis of nanostructures, especially in large Acenes need high money and time, a model for predicting the physical and electronic properties is of special importance. Topological indices that were introduced during the studies on the molecular graphs in chemistry can describe and predict some chemical, physical, electronic of the molecules. This paper explains and proves some theorem and then examines topological index F (G) in the linear Acenes family. It is tried to provide an appropriate model to determine the amounts of total π electron energy in the family, and especially for the members where the number of loops are high.

scholarly journals Computing Correlation among the Graphs under Lexicographic Product via Zagreb Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-17
Author(s):  
Muhammad Javaid ◽  
Saira Javed ◽  
Yasmene F. Alanazi ◽  
Abdulaziz Mohammed Alanazi
Keyword(s):  
Topological Index ◽  
Chemical Properties ◽  
Lexicographic Product ◽  
Statistical Tools ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Molecule Structure ◽  
Polygonal Chains ◽  
Computing Correlation ◽  
And Chemical Properties

A topological index (TI) is a numerical descriptor of a molecule structure or graph that predicts its different physical, biological, and chemical properties in a theoretical way avoiding the difficult and costly procedures of chemical labs. In this paper, for two connected (molecular) graphs G 1 and G 2 , we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs T k G 1 and G 2 , where T k G 1 is obtained by applying the generalized total operation T k on G 1 with k ≥ 1 as some integral value. Moreover, we compute the different degree-based TIs such as first Zagreb, second Zagreb, forgotten Zagreb, and hyper-Zagreb. In the end, a comparison among all the aforesaid TIs is also conducted with the help of certain statistical tools for some particular families of generalized total-sum graphs under lexicographic product.

scholarly journals F-Index of some graph operations

2016 ◽  
Vol 08 (02) ◽  
pp. 1650025 ◽  
Author(s):  
Nilanjan De ◽  
Sk. Md. Abu Nayeem ◽  
Anita Pal
Keyword(s):  
Electron Energy ◽  
Topological Index ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Molecular Graphs ◽  
Basic Properties ◽  
Graph Operations ◽  
Physico Chemical ◽  
Vertex Degrees

The F-index of a graph is defined as the sum of cubes of the vertex degrees of the graph. This was introduced in 1972, in the same paper where the first and second Zagreb indices were introduced to study the structure-dependency of total [Formula: see text]-electron energy. But this topological index was not further studied till then. Very recently, Furtula and Gutman [A forgotten topological index,J. Math. Chem. 53(4) (2015) 1184–1190.] reinvestigated the index and named it “forgotten topological index” or “F-index”. In that paper, they present some basic properties of this index and showed that this index can enhance the physico-chemical applicability of Zagreb index. Here, we study the behavior of this index under several graph operations and apply our results to find the F-index of different chemically interesting molecular graphs and nanostructures.

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 Eccentricity-Based Topological Invariants of Some Chemical Graphs

Atoms ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 21 ◽  
Author(s):  
Nazeran Idrees ◽  
Muhammad Saif ◽  
Tehmina Anwar
Keyword(s):  
Boiling Point ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Topological Indices ◽  
Topological Invariants ◽  
Circulant Graphs ◽  
Eccentric Connectivity Index ◽  
Molecular Graphs ◽  
Eccentricity Index ◽  
Physical And Chemical

Topological index is an invariant of molecular graphs which correlates the structure with different physical and chemical invariants of the compound like boiling point, chemical reactivity, stability, Kovat’s constant etc. Eccentricity-based topological indices, like eccentric connectivity index, connective eccentric index, first Zagreb eccentricity index, and second Zagreb eccentricity index were analyzed and computed for families of Dutch windmill graphs and circulant graphs.

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