On Degree-Based Topological Indices of Symmetric Chemical Structures

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randić index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.

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Computing topological polynomials of mesh-derived networks

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500775 ◽

2018 ◽

Vol 10 (06) ◽

pp. 1850077 ◽

Cited By ~ 6

Author(s):

Muhammad Imran ◽

Abdul Qudair Baig ◽

Shafiq Ur Rehman ◽

Haidar Ali ◽

Roslan Hasni

Keyword(s):

Mesh Networks ◽

Molecular Graph ◽

Chemical Properties ◽

Chemical Compounds ◽

Topological Descriptors ◽

Cut Edge ◽

Physico Chemical ◽

First Time ◽

Ga Index ◽

Atom Bond

Topological descriptors are numerical parameters of a molecular graph which characterize its molecular topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randić, atom-bond connectivity [Formula: see text] and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. The counting polynomials are those polynomials having at exponent the extent of a property partition and coefficients the multiplicity/occurrence of the corresponding partition. All of the studied interconnection mesh networks in this paper are motivated by the molecular structure of a Sodium chloride NaCl. In this paper, Omega, Sadhana and PI polynomials are computed for mesh-derived networks. These polynomials were proposed on the ground of quasi-orthogonal cut edge strips in polycyclic graphs. These polynomials count equidistant and non-equidistant edges in graphs. Moreover, the analytical closed formulas of these polynomials for mesh-derived networks are computed for the first time.

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Topological characterization of dendrimer, benzenoid, and nanocone

Zeitschrift für Naturforschung C ◽

10.1515/znc-2018-0153 ◽

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.

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Topological aspects of some dendrimer structures

Nanotechnology Reviews ◽

10.1515/ntrev-2017-0184 ◽

2018 ◽

Vol 7 (2) ◽

pp. 123-129 ◽

Cited By ~ 14

Author(s):

Adnan Aslam ◽

Muhammad Kamran Jamil ◽

Wei Gao ◽

Waqas Nazeer

Keyword(s):

Self Assembly ◽

Molecular Graph ◽

Chemical Properties ◽

Topological Indices ◽

Connectivity Index ◽

Molecular Topology ◽

Zinc Porphyrin ◽

Physico Chemical ◽

Randić Connectivity Index ◽

Atom Bond

AbstractA numerical number associated to the molecular graphGthat describes its molecular topology is called topological index. In the study ofQSARandQSPR, topological indices such as atom-bond connectivity index, Randić connectivity index, geometric index, etc. help to predict many physico-chemical properties of the chemical compound under study. Dendrimers are macromolecules and have many applications in chemistry, especially in self-assembly procedures and host-guest reactions. The aim of this report is to compute degree-based topological indices, namely the fourth atom-bond connectivity index and fifth geometric arithmetic index of poly propyl ether imine, zinc porphyrin, and porphyrin dendrimers.

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On topological properties of dominating David derived networks

Canadian Journal of Chemistry ◽

10.1139/cjc-2015-0185 ◽

2016 ◽

Vol 94 (2) ◽

pp. 137-148 ◽

Cited By ~ 10

Author(s):

Muhammad Imran ◽

Abdul Qudair Baig ◽

Haidar Ali

Keyword(s):

Interconnection Networks ◽

Network Science ◽

Chemical Properties ◽

Chemical Compounds ◽

Topological Indices ◽

Molecular Topology ◽

Topological Properties ◽

Graph Invariant ◽

Physico Chemical ◽

Atom Bond

Topological indices are numerical parameters of a graph that characterize its molecular topology and are usually graph invariant. In a QSAR/QSPR study, the physico-chemical properties and topological indices such as the Randić, atom–bond connectivity (ABC), and geometric–arithmetic (GA) indices are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this important area of research. All of the studied interconnection networks in this paper are constructed by the Star of David network. In this paper, we study the general Randić, first Zagreb, ABC, GA, ABC4 and GA5, indices for the first, second, and third types of dominating David derived networks and give closed formulas of these indices for these networks. These results are useful in network science to understand the underlying topologies of these networks.

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COMPUTING TOPOLOGICAL INDICES OF SiO2 LAYER STRUCTURE AND BENZENOID SERIES

Latin American Applied Research - An international journal ◽

10.52292/j.laar.2019.197 ◽

2019 ◽

Vol 49 (4) ◽

pp. 219-224

Author(s):

M. H. Muhammad ◽

Juan Luis Garcia Guirao ◽

N. A. Rehman ◽

M. K. Siddiqui

Keyword(s):

Strain Energy ◽

Layer Structure ◽

Molecular Graph ◽

Chemical Properties ◽

Chemical Compounds ◽

Topological Indices ◽

Sio2 Layer ◽

Physico Chemical ◽

Forgotten Index ◽

Map Operations

A molecular graph can be transformed using map operations, one of these, named Capra, being defined by Diudea (2005). Topological indices are closely related to the toxicological, physicochemical, pharmacological properties of a chemical compound. These topological indices correlate certain physico-chemical properties like boiling point, stability and strain energy of chemical compounds. In this paper, we focus on the Silicate SiO2 layer structure and the structure of Capra-designed planar benzenoid series , (). We determined Zagreb type indices, Forgotten index, Augmented index and Balaban index for these structures.

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Topological Indices of mth Chain Silicate Graphs

Mathematics ◽

10.3390/math7010042 ◽

2019 ◽

Vol 7 (1) ◽

pp. 42 ◽

Cited By ~ 2

Author(s):

Jia-Bao Liu ◽

Muhammad Kashif Shafiq ◽

Haidar Ali ◽

Asim Naseem ◽

Nayab Maryam ◽

...

Keyword(s):

Biological Activity ◽

Chemical Structure ◽

Chemical Properties ◽

Chemical Compounds ◽

Topological Indices ◽

Numerical Representation ◽

Topological Descriptor ◽

Physico Chemical ◽

Chain Silicate ◽

Atom Bond

A topological index is a numerical representation of a chemical structure, while a topological descriptor correlates certain physico-chemical characteristics of underlying chemical compounds besides its numerical representation. A large number of properties like physico-chemical properties, thermodynamic properties, chemical activity, and biological activity are determined by the chemical applications of graph theory. The biological activity of chemical compounds can be constructed by the help of topological indices such as atom-bond connectivity (ABC), Randić, and geometric arithmetic (GA). In this paper, Randić, atom bond connectivity (ABC), Zagreb, geometric arithmetic (GA), ABC4, and GA5 indices of the mth chain silicate S L ( m , n ) network are determined.

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On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

Symmetry ◽

10.3390/sym10080320 ◽

2018 ◽

Vol 10 (8) ◽

pp. 320 ◽

Cited By ~ 12

Author(s):

Young Kwun ◽

Abaid Virk ◽

Waqas Nazeer ◽

M. Rehman ◽

Shin Kang

Keyword(s):

Molecular Structure ◽

Graph Theory ◽

Molecular Graph ◽

Chemical Properties ◽

Topological Indices ◽

Molecular Compound ◽

Zagreb Indices ◽

Silicon Carbon ◽

Physico Chemical ◽

Structure Research

The application of graph theory in chemical and molecular structure research has far exceeded people’s expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonds by edges. Topological indices help us to predict many physico-chemical properties of the concerned molecular compound. In this article, we compute Generalized first and multiplicative Zagreb indices, the multiplicative version of the atomic bond connectivity index, and the Generalized multiplicative Geometric Arithmetic index for silicon-carbon Si2C3−I[p,q] and Si2C3−II[p,q] second.

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On the Multiplicative Degree-Based Topological Indices of Silicon-Carbon Si2C3-I[p,q] and Si2C3-II[p,q]

10.20944/preprints201806.0066.v1 ◽

2018 ◽

Author(s):

Young Chel Kwun ◽

Abaid ur Rehman Virk ◽

Waqas Nazeer ◽

Shin Min Kang

Keyword(s):

Molecular Structure ◽

Graph Theory ◽

Molecular Graph ◽

Chemical Properties ◽

Topological Indices ◽

Molecular Compound ◽

Silicon Carbon ◽

Physico Chemical ◽

Structure Research

The application of graph theory in chemical and molecular structure research far exceeds people's expectations, and it has recently grown exponentially. In the molecular graph, atoms are represented by vertices and bonded by edges. Closed forms of multiplicative degree-based topological indices which are numerical parameters of the structure and determine physico-chemical properties of the concerned molecular compound. In this article, we compute and analyze many multiplicative degree-based topological indices of silicon-carbon Si2C3-I[p,q] and Si2C3-II[p,q].

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M-Polynomial and Degree Based Topological Indices of Some Nanostructures

Symmetry ◽

10.3390/sym12050831 ◽

2020 ◽

Vol 12 (5) ◽

pp. 831 ◽

Cited By ~ 7

Author(s):

Zahid Raza ◽

Mark Essa K. Sukaiti

Keyword(s):

Graphical Representation ◽

Chemical Properties ◽

Chemical Compounds ◽

Detailed Comparison ◽

Topological Indices ◽

Chemical Structures

The association of M-polynomial to chemical compounds and chemical networks is a relatively new idea, and it gives good results about the topological indices. These results are then used to correlate the chemical compounds and chemical networks with their chemical properties and bioactivities. In this paper, an effort is made to compute the general form of the M-polynomials for two classes of dendrimer nanostars and four types of nanotubes. These nanotubes have very nice symmetries in their structural representations, which have been used to determine the corresponding M-polynomials. Furthermore, by using the general form of M-polynomial of these nanostructures, some degree-based topological indices have been computed. In the end, the graphical representation of the M-polynomials is shown, and a detailed comparison between the obtained topological indices for aforementioned chemical structures is discussed.

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Topological indices of rhombus type silicate and oxide networks

Canadian Journal of Chemistry ◽

10.1139/cjc-2016-0486 ◽

2017 ◽

Vol 95 (2) ◽

pp. 134-143 ◽

Cited By ~ 9

Author(s):

M. Javaid ◽

Masood Ur Rehman ◽

Jinde Cao

Keyword(s):

Molecular Graph ◽

Chemical Compounds ◽

Quantitative Structure Activity Relationship ◽

Topological Indices ◽

Quantitative Structure ◽

Structure Property ◽

Structure Activity ◽

Structure Property Relationship ◽

Cartesian Coordinate ◽

Atom Bond

For a molecular graph, a numeric quantity that characterizes the whole structure of a graph is called a topological index. In the studies of quantitative structure – activity relationship (QSAR) and quantitative structure – property relationship (QSPR), topological indices are utilized to guess the bioactivity of chemical compounds. In this paper, we compute general Randić, first general Zagreb, generalized Zagreb, multiplicative Zagreb, atom-bond connectivity (ABC), and geometric arithmetic (GA) indices for the rhombus silicate and rhombus oxide networks. In addition, we also compute the latest developed topological indices such as the fourth version of ABC (ABC4), the fifth version of GA (GA5), augmented Zagreb, and Sanskruti indices for the foresaid networks. At the end, a comparison between all the indices is included, and the result is shown with the help of a Cartesian coordinate system.

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