scholarly journals Bounds on the Arithmetic-Geometric Index

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 689
Author(s):  
José M. Rodríguez ◽  
José L. Sánchez ◽  
José M. Sigarreta ◽  
Eva Tourís
Keyword(s):  
Maximum Degree ◽  
Minimum Degree ◽  
Point Of View ◽  
Extremal Graphs ◽  
Zagreb Index ◽  
Star Graphs ◽  
Practical Point ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Atom Bond

The concept of arithmetic-geometric index was recently introduced in chemical graph theory, but it has proven to be useful from both a theoretical and practical point of view. The aim of this paper is to obtain new bounds of the arithmetic-geometric index and characterize the extremal graphs with respect to them. Several bounds are based on other indices, such as the second variable Zagreb index or the general atom-bond connectivity index), and some of them involve some parameters, such as the number of edges, the maximum degree, or the minimum degree of the graph. In most bounds, the graphs for which equality is attained are regular or biregular, or star graphs.

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 Topological Indices of H-Naphtalenic Nanosheet

2018 ◽  
Vol 16 (1) ◽  
pp. 1184-1188 ◽  
Author(s):  
Nazeran Idrees ◽  
Muhammad Jawwad Saif ◽  
Afshan Sadiq ◽  
Asia Rauf ◽  
Fida Hussain
Keyword(s):  
Chemical Structure ◽  
Topological Indices ◽  
Connectivity Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Second Zagreb Index ◽  
Topological Descriptor ◽  
Chemical Graph Theory ◽  
Atom Bond

AbstractIn chemical graph theory, a single numeric number related to a chemical structure is called a topological descriptor or topological index of a graph. In this paper, we compute analytically certain topological indices for H-Naphtalenic nanosheet like Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper-Zagreb index using edge partition technique. The first multiple Zagreb index and the second multiple Zagreb index of the nanosheet are also discussed in this paper.

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.

scholarly journals The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

2021 ◽  
pp. 54-75
Author(s):  
Mohammed Alsharafi ◽  
Yusuf Zeren ◽  
Abdu Alameri
Keyword(s):  
Graph Theory ◽  
Cartesian Product ◽  
Quantitative Structure Activity Relationship ◽  
Quantitative Structure ◽  
Structure Property ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Strong Product ◽  
Chemical Graph Theory ◽  
Mathematical Operations

In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.

scholarly journals On Some Ve-Degree and Harmonic Molecular Topological Properties of Carborundum

2020 ◽  
Vol 8 (1) ◽  
pp. 65
Author(s):  
Murat Cancan ◽  
Kerem Yamaç ◽  
Ziyattin Taş ◽  
Mehmet Şerif Aldemir
Keyword(s):  
Silicon Carbide ◽  
Graph Theory ◽  
Topological Indices ◽  
Topological Properties ◽  
Degree Sum ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Degree Harmonic ◽  
Atom Bond

Carborundum, also known as silicon carbide which containing carbon and silicon, is a semiconductor. Molecular topological properties of physical substances are important tools to investigate the underlying topology of these substances. Ev-degree and ve-degree based on the molecular topological indices have been defined as parallel to their corresponding classical degree based topological indices in chemical graph theory. Classical degree based topological properties of carborundum have been investigated recently. As a continuation of these studies, in this study, we compute novel ve-degree harmonic, ve-degree sum-connectivity, ve-degree geometric-arithmetic, and ve-degree atom-bond connectivity, the first and the fifth harmonic molecular topological indices of two carborundum structures. 

scholarly journals MULTIPLICATIVE CONNECTIVITY STATUS NEIGHBORHOOD INDICES OF GRAPHS

2020 ◽  
Vol 9 (12) ◽  
pp. 59-68
Keyword(s):  
Graph Theory ◽  
Chemical Characteristics ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Connectivity Indices ◽  
Atom Bond ◽  
Multiplicative Arithmetic

The connectivity indices are applied to measure the chemical characteristics of compounds in Chemical Graph Theory. In this paper, we introduce the multiplicative atom bond connectivity status neighborhood index, multiplicative geometric-arithmetic status neighborhood index, multiplicative arithmetic-geometric status neighborhood index, multiplicative augmented status neighborhood index of a graph. Also we compute these newly defined indices for some standard graphs, wheel and friendship graphs.

scholarly journals The Generalized Zagreb Index of Some Carbon Structures

2018 ◽  
Vol 26 (1) ◽  
pp. 91-104 ◽  
Author(s):  
Prosanta Sarkar ◽  
Nilanjan De ◽  
Anita Pal
Keyword(s):  
Graph Theory ◽  
Physicochemical Properties ◽  
Topological Indices ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Carbon Structures

Abstract In chemical graph theory, chemical structures are model edthrough a graph where atoms are considered as vertices and edges are bonds between them. In chemical sciences, topological indices are used for understanding the physicochemical properties of molecules. In this work, we study the generalized Zagreb index for three types of carbon allotrope’s theoretically.

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 Existence of solutions for a class of nonlinear boundary value problems on the hexasilinane graph

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Ali Turab ◽  
Zoran D. Mitrović ◽  
Ana Savić
Keyword(s):  
Boundary Value Problems ◽  
Nonlinear Boundary ◽  
Existence Of Solutions ◽  
Boundary Value ◽  
Chemical Formula ◽  
Nonlinear Boundary Value Problems ◽  
Star Graphs ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Fractional Boundary Value Problems

AbstractChemical graph theory is a field of mathematics that studies ramifications of chemical network interactions. Using the concept of star graphs, several investigators have looked into the solutions to certain boundary value problems. Their choice to utilize star graphs was based on including a common point connected to other nodes. Our aim is to expand the range of the method by incorporating the graph of hexasilinane compound, which has a chemical formula $\mathrm{H}_{12} \mathrm{Si}_{6}$ H 12 Si 6 . In this paper, we examine the existence of solutions to fractional boundary value problems on such graphs, where the fractional derivative is in the Caputo sense. Finally, we include an example to support our significant findings.

Inverse Sum Indeg Index of Subdivision, t-Subdivision Graphs, and Related Sums

2020 ◽  
pp. 104-119 ◽  
Author(s):  
Amitav Doley ◽  
Jibonjyoti Buragohain ◽  
A. Bharali
Keyword(s):  
Surface Area ◽  
Maximum Degree ◽  
Minimum Degree ◽  
Total Surface Area ◽  
Upper Bounds ◽  
Lower And Upper Bounds ◽  
Zagreb Index ◽  
Octane Isomers ◽  
Graph Parameters ◽  
The First Zagreb Index

The inverse sum indeg (ISI) index of a graph G is defined as the sum of the weights dG(u)dG(v)/dG(u)+dG(v) of all edges uv in G, where dG(u) is the degree of the vertex u in G. This index is found to be a significant predictor of total surface area of octane isomers. In this chapter, the authors present some lower and upper bounds for ISI index of subdivision graphs, t-subdivision graphs, s-sum and st -sum of graphs in terms of some graph parameters such as order, size, maximum degree, minimum degree, and the first Zagreb index. The extremal graphs are also characterized for their sharpness.

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