scholarly journals On topological properties of block shift and hierarchical hypercube networks

Open Physics ◽  
2018 ◽  
Vol 16 (1) ◽  
pp. 810-819
Author(s):  
Juan Luis García Guirao ◽  
Muhammad Kamran Siddiqui ◽  
Asif Hussain
Keyword(s):  
Graph Theory ◽  
Interconnection Networks ◽  
Communication Theory ◽  
Chemical Reactivity ◽  
Zagreb Index ◽  
Electronic Engineering ◽  
Chemical Graph Theory ◽  
Chemical Constitution ◽  
Vertex Degrees ◽  
Hypercube Networks

Abstract Networks play an important role in electrical and electronic engineering. It depends on what area of electrical and electronic engineering, for example there is a lot more abstract mathematics in communication theory and signal processing and networking etc. Networks involve nodes communicating with each other. Graph theory has found a considerable use in this area of research. A topological index is a real number associated with chemical constitution purporting for correlation of chemical networks with various physical properties, chemical reactivity. The concept of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index and Zagreb polynomials was established in chemical graph theory based on vertex degrees. In this paper, we extend this study to interconnection networks and derive analytical closed results of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, Zagreb polynomials and redefined Zagreb indices for block shift network (BSN − 1) and (BSN − 2), hierarchical hypercube (HHC − 1) and (HHC − 2).

scholarly journals Molecular Descriptors of Nanotube, Oxide, Silicate, and Triangulene Networks

2017 ◽  
Vol 2017 ◽  
pp. 1-10 ◽  
Author(s):  
Wei Gao ◽  
Muhammad Kamran Siddiqui
Keyword(s):  
Molecular Structure ◽  
Carbon Nanotube ◽  
Interconnection Networks ◽  
Chemical Structure ◽  
Chemical Reactivity ◽  
Hexagonal Lattice ◽  
Zagreb Index ◽  
Chemical Graph Theory ◽  
Vertex Degrees ◽  
Carbon Nanotube Networks

A topological index is a real number associated with chemical constitution purporting for correlation of chemical structure with various physical properties, chemical reactivity, or biological activity. The concept of hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials was established in chemical graph theory based on vertex degrees. It is reported that these indices are useful in the study of anti-inflammatory activities of certain chemical networks. In this paper, we study carbon nanotube networks which are motivated by molecular structure of regular hexagonal lattice and also studied interconnection networks which are motivated by molecular structure of a chemical compound SiO4. We determine hyper Zagreb index, first multiple Zagreb index, second multiple Zagreb index, and Zagreb polynomials for some important class of carbon nanotube networks, dominating oxide network, dominating silicate network, and regular triangulene oxide network.

scholarly journals Irregularity of Block Shift Networks and Hierarchical Hypercube Networks

2019 ◽  
Vol 2019 ◽  
pp. 1-12
Author(s):  
Juanyan Fang ◽  
Iftikhar Ahmed ◽  
Abid Mehboob ◽  
Kashif Nazar ◽  
Haseeb Ahmad
Keyword(s):  
Signal Processing ◽  
Graph Theory ◽  
Communication Theory ◽  
Parallel Applications ◽  
Planning Systems ◽  
Electronic Engineering ◽  
System Graph ◽  
Hypercube Networks ◽  
Ideal Method ◽  
Connection Cost

There is extremely a great deal of mathematics associated with electrical and electronic engineering. It relies upon what zone of electrical and electronic engineering; for instance, there is much increasingly theoretical mathematics in communication theory, signal processing and networking, and so forth. Systems include hubs speaking with one another. A great deal of PCs connected together structure a system. Mobile phone clients structure a network. Networking includes the investigation of the most ideal method for executing a system. Graph theory has discovered a significant use in this zone of research. In this paper, we stretch out this examination to interconnection systems. Hierarchical interconnection systems (HINs) give a system to planning systems with diminished connection cost by exploiting the area of correspondence that exists in parallel applications. HINs utilize numerous levels. Lower-level systems give nearby correspondence, while more significant level systems encourage remote correspondence. HINs provide issue resilience within the sight of some defective nodes and additionally interfaces. Existing HINs can be comprehensively characterized into two classes: those that use nodes or potential interface replication and those that utilize reserve interface nodes.

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 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 Reformulated Zagreb Indices of Some Derived Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (4) ◽  
pp. 366 ◽  
Author(s):  
Jia-Bao Liu ◽  
Bahadur Ali ◽  
Muhammad Aslam Malik ◽  
Hafiz Muhammad Afzal Siddiqui ◽  
Muhammad Imran
Keyword(s):  
Physical Properties ◽  
Chemical Structure ◽  
Topological Index ◽  
Chemical Reactivity ◽  
Line Graph ◽  
Total Graph ◽  
Zagreb Indices ◽  
Subdivision Graph ◽  
Chemical Constitution ◽  
Vertex Degrees

A topological index is a numeric quantity that is closely related to the chemical constitution to establish the correlation of its chemical structure with chemical reactivity or physical properties. Miličević reformulated the original Zagreb indices in 2004, replacing vertex degrees by edge degrees. In this paper, we established the expressions for the reformulated Zagreb indices of some derived graphs such as a complement, line graph, subdivision graph, edge-semitotal graph, vertex-semitotal graph, total graph, and paraline graph of a graph.

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 The (a,b)-Zagreb index of line graphs of subdivision graphs of some molecular structures

2020 ◽  
pp. 1-9
Author(s):  
Prosanta Sarkar ◽  
Anita Pal ◽  
Nilanjan De
Keyword(s):  
Chemical Structure ◽  
Molecular Structures ◽  
Line Graphs ◽  
Zagreb Index ◽  
Physiochemical Properties ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Chemical Constitution ◽  
Structure Descriptor

A graph is a mathematical model used to predict the topology of a given system. In chemical graph theory, a graph is designed by considering atoms as vertices and edges as bonds between atoms of a particular molecule. A topological index or molecular structure descriptor is a numeric quantity associated with the chemical constitution which correlated with various physiochemical properties of the chemical structure. In this paper, we study the [Formula: see text]-Zagreb index of line graphs of the subdivision graphs of some chemical structures.

scholarly journals Molecular description of copper(II) oxide

2017 ◽  
Vol 36 (1) ◽  
Author(s):  
Mohammad Reza Farahani ◽  
Wei Gao ◽  
Abdul Qudair Baig ◽  
Wasaq Khalid
Keyword(s):  
Graph Theory ◽  
Molecular Graph ◽  
Theoretical Chemistry ◽  
Topological Descriptors ◽  
Zagreb Index ◽  
Chemical Graph ◽  
Mathematical Chemistry ◽  
Chemical Graph Theory ◽  
Numerical Invariants ◽  
Molecular Description

Graph theory has much advancement in the field of mathematical chemistry. Recently, chemical graph theory has become very popular among researchers because of its wide applications in mathematical chemistry. The molecular topological descriptors are the numerical invariants of a molecular graph and are very useful for predicting their bioactivity. A great variety of such indices are studied and used in theoretical chemistry, pharmaceutical researchers, in drugs and in different other fields.In this article, we study the chemical graph of copper oxide and compute degree based topological indices mainly ABC, GA, ABC4, GA5, general Randić index and Zagreb index for copper(II) oxide, CuO. Furthermore, we give exact formulas of these indices which are helpful in studying the underlying topologies.

scholarly journals Topological Indices of Some New Graph Operations and Their Possible Applications

2021 ◽  
pp. 16-30
Author(s):  
Abdu Qaid Saif Alameri ◽  
Mohammed Saad Yahya Al-Sharafi
Keyword(s):  
Graph Theory ◽  
Chemical Compounds ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Structural Invariant ◽  
Graph Operations ◽  
Chemical Graph Theory ◽  
Cyclic Alkanes ◽  
The First Zagreb Index

A chemical graph theory is a fascinating branch of graph theory which has many applications related to chemistry. A topological index is a real number related to a graph, as its considered a structural invariant. It’s found that there is a strong correlation between the properties of chemical compounds and their topological indices. In this paper, we introduce some new graph operations for the first Zagreb index, second Zagreb index and forgotten index "F-index". Furthermore, it was found some possible applications on some new graph operations such as roperties of molecular graphs that resulted by alkanes or cyclic alkanes.

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