scholarly journals The Bounds for the First General Zagreb Index of a Graph

2021 ◽  
Author(s):  
Rao Lİ
Keyword(s):  
Zagreb Index

On Hyper-Zagreb Index of Three Graph Operations

2019 ◽  
Vol 10 (2) ◽  
pp. 301-309
Author(s):  
A. Bharali ◽  
Amitav Doley
Keyword(s):  
Zagreb Index ◽  
Graph Operations

On reduced second Zagreb index

2020 ◽  
Vol 39 (3) ◽  
pp. 776-791 ◽  
Author(s):  
Lkhagva Buyantogtokh ◽  
Batmend Horoldagva ◽  
Kinkar Chandra Das
Keyword(s):  
Zagreb Index ◽  
Second Zagreb Index

scholarly journals On multiplicative degree based topological indices for planar octahedron networks

2020 ◽  
Vol 43 (1) ◽  
pp. 219-228
Author(s):  
Ghulam Dustigeer ◽  
Haidar Ali ◽  
Muhammad Imran Khan ◽  
Yu-Ming Chu
Keyword(s):  
Graph Theory ◽  
Information Science ◽  
Biological Activities ◽  
Molecular Graph ◽  
Triangular Prism ◽  
Structure Property ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Chemical Graph Theory ◽  
Analytical Formulas

AbstractChemical graph theory is a branch of graph theory in which a chemical compound is presented with a simple graph called a molecular graph. There are atomic bonds in the chemistry of the chemical atomic graph and edges. The graph is connected when there is at least one connection between its vertices. The number that describes the topology of the graph is called the topological index. Cheminformatics is a new subject which is a combination of chemistry, mathematics and information science. It studies quantitative structure-activity (QSAR) and structure-property (QSPR) relationships that are used to predict the biological activities and properties of chemical compounds. We evaluated the second multiplicative Zagreb index, first and second universal Zagreb indices, first and second hyper Zagreb indices, sum and product connectivity indices for the planar octahedron network, triangular prism network, hex planar octahedron network, and give these indices closed analytical formulas.

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.

Topological characterization of dendrimer, benzenoid, and nanocone

2018 ◽  
Vol 74 (1-2) ◽  
pp. 35-43
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui ◽  
Najma Abdul Rehman ◽  
Mehwish Hussain Muhammad
Keyword(s):  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Zagreb Index ◽  
Topological Characterization ◽  
Complex Molecules ◽  
Chemical Structures ◽  
Physico Chemical ◽  
Quantitative Structure Activity Relationships

Abstract Dendrimers are large and complex molecules with very well defined chemical structures. More importantly, dendrimers are highly branched organic macromolecules with successive layers or generations of branch units surrounding a central core. Topological indices are numbers associated with molecular graphs for the purpose of allowing quantitative structure-activity relationships. These topological indices correlate certain physico-chemical properties such as the boiling point, stability, strain energy, and others, of chemical compounds. In this article, we determine hyper-Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for hetrofunctional dendrimers, triangular benzenoids, and nanocones.

scholarly journals Multiplicative Zagreb indices of cacti

2016 ◽  
Vol 08 (03) ◽  
pp. 1650040 ◽  
Author(s):  
Shaohui Wang ◽  
Bing Wei
Keyword(s):  
Graph Theory ◽  
Lower Bounds ◽  
Connected Graph ◽  
Upper And Lower Bounds ◽  
Extremal Graphs ◽  
Zagreb Index ◽  
Zagreb Indices ◽  
Material Chemistry ◽  
Cactus Graph ◽  
Cactus Graphs

Let [Formula: see text] be multiplicative Zagreb index of a graph [Formula: see text]. A connected graph is a cactus graph if and only if any two of its cycles have at most one vertex in common, which is a generalization of trees and has been the interest of researchers in the field of material chemistry and graph theory. In this paper, we use a new tool to obtain the upper and lower bounds of [Formula: see text] for all cactus graphs and characterize the corresponding extremal graphs.

On the first Zagreb Index of Polygraphs

2014 ◽  
Vol 45 ◽  
pp. 147-151 ◽  
Author(s):  
Hossein Shabani ◽  
Reza Kahkeshani
Keyword(s):  
First Zagreb Index ◽  
Zagreb Index ◽  
The First Zagreb Index

scholarly journals Maximizing and Minimizing Multiplicative Zagreb Indices of Graphs Subject to Given Number of Cut Edges

Mathematics ◽  
2018 ◽  
Vol 6 (11) ◽  
pp. 227 ◽  
Author(s):  
Shaohui Wang ◽  
Chunxiang Wang ◽  
Lin Chen ◽  
Jia-Bao Liu ◽  
Zehui Shao
Keyword(s):  
Molecular Graph ◽  
Zagreb Index ◽  
Zagreb Indices

Given a (molecular) graph, the first multiplicative Zagreb index Π 1 is considered to be the product of squares of the degree of its vertices, while the second multiplicative Zagreb index Π 2 is expressed as the product of endvertex degree of each edge over all edges. We consider a set of graphs G n , k having n vertices and k cut edges, and explore the graphs subject to a number of cut edges. In addition, the maximum and minimum multiplicative Zagreb indices of graphs in G n , k are provided. We also provide these graphs with the largest and smallest Π 1 ( G ) and Π 2 ( G ) in G n , k .

scholarly journals Polynomials and General Degree-Based Topological Indices of Generalized Sierpinski Networks

Complexity ◽  
2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Chengmei Fan ◽  
M. Mobeen Munir ◽  
Zafar Hussain ◽  
Muhammad Athar ◽  
Jia-Bao Liu
Keyword(s):  
Complex Systems ◽  
Computer Science ◽  
Topological Indices ◽  
Fractal Nature ◽  
Similar Nature ◽  
Zagreb Index ◽  
Recursive Sequences ◽  
And Mathematics

Sierpinski networks are networks of fractal nature having several applications in computer science, music, chemistry, and mathematics. These networks are commonly used in chaos, fractals, recursive sequences, and complex systems. In this article, we compute various connectivity polynomials such as M -polynomial, Zagreb polynomials, and forgotten polynomial of generalized Sierpinski networks S k n and recover some well-known degree-based topological indices from these. We also compute the most general Zagreb index known as α , β -Zagreb index and several other general indices of similar nature for this network. Our results are the natural generalizations of already available results for particular classes of such type of networks.

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.

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