scholarly journals Molecular topological invariants of certain chemical networks

2021 ◽  
Vol 44 (1) ◽  
pp. 141-149
Author(s):  
Syed Ahtsham Ul Haq Bokhary ◽  
Muhammad Imran ◽  
Shehnaz Akhter ◽  
Sadia Manzoor
Keyword(s):  
Chemical Compounds ◽  
Topological Descriptors ◽  
Discrete Mathematics ◽  
Chemical Characteristics ◽  
Topological Invariants ◽  
Molecular Topology ◽  
Graph Invariants ◽  
Physico Chemical ◽  
Structure Relationship ◽  
Atom Bond

Abstract Topological descriptors are the graph invariants that are used to explore the molecular topology of the molecular/chemical graphs. In QSAR/QSPR research, physico-chemical characteristics and topological invariants including Randić, atom-bond connectivity, and geometric arithmetic invariants are utilized to corelate and estimate the structure relationship and bioactivity of certain chemical compounds. Graph theory and discrete mathematics have discovered an impressive utilization in the area of research. In this article, we investigate the valency-depended invariants for certain chemical networks like generalized Aztec diamonds and tetrahedral diamond lattice. Moreover, the exact values of invariants for these categories of chemical networks are derived.

scholarly journals On topological properties of dominating David derived networks

2016 ◽  
Vol 94 (2) ◽  
pp. 137-148 ◽  
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.

Computing topological polynomials of mesh-derived networks

2018 ◽  
Vol 10 (06) ◽  
pp. 1850077 ◽  
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.

On degree-based topological descriptors of strong product graphs

2016 ◽  
Vol 94 (6) ◽  
pp. 559-565 ◽  
Author(s):  
Shehnaz Akhter ◽  
Muhammad Imran
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Zagreb Indices ◽  
Strong Product ◽  
Product Graphs ◽  
Product Of Graphs ◽  
Atom Bond

Topological descriptors are numerical parameters of a graph that characterize its topology and are usually graph invariant. In a QSAR/QSPR study, physicochemical properties and topological indices such as Randić, atom–bond connectivity, and geometric–arithmetic are used to predict the bioactivity of different chemical compounds. There are certain types of topological descriptors such as degree-based topological indices, distance-based topological indices, counting-related topological indices, etc. Among degree-based topological indices, the so-called atom–bond connectivity and geometric–arithmetic are of vital importance. These topological indices correlate certain physicochemical properties such as boiling point, stability, strain energy, etc., of chemical compounds. In this paper, analytical closed formulas for Zagreb indices, multiplicative Zagreb indices, harmonic index, and sum-connectivity index of the strong product of graphs are determined.

Topological aspects of some dendrimer structures

2018 ◽  
Vol 7 (2) ◽  
pp. 123-129 ◽  
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.

scholarly journals Eccentricity based topological indices of siloxane and POPAM dendrimers

2020 ◽  
Vol 43 (1) ◽  
pp. 92-98
Author(s):  
Muhammad Azhar Iqbal ◽  
Muhammad Imran ◽  
Muhammad Asad Zaighum
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Molecular Structures ◽  
Topological Descriptors ◽  
Physico Chemical ◽  
Early Drug

AbstractA massive of early drug tests indicates that there is some strong inner connections among the bio-medical and pharmacology properties of nanostar dendrimers and their molecular structures. Topological descriptors are presented as fundamentally transforming a molecular graph into a number. There exist various categories of such descriptors particularly those descriptors that based on edge and vertex distances. Topological descriptors are exercised for designing biological, physico-chemical, toxicological, pharmacologic and other characteristics of chemical compounds. In this paper, we study infinite classes of siloxane and POPAM dendrimers and derive their Zagreb eccentricity indices, eccentric-connectivity and total-eccentricity indices.

scholarly journals Locating and Multiplicative Locating Indices of Graphs with QSPR Analysis

2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Suha Wazzan ◽  
Anwar Saleh
Keyword(s):  
Melting Point ◽  
Linear Regression ◽  
Boiling Point ◽  
Chemical Compounds ◽  
Chemical Characteristics ◽  
Physico Chemical

In this paper, by introducing a new version of locating indices called multiplicative locating indices, we compute exact values of these indices on well-known families of graphs and graphs obtained by some operations. Also, we determine the importance of locating and multiplicative locating indices of hexane and its isomers. Furthermore, we show that locating indices actually have a reasonable correlation using linear regression with physico-chemical characteristics such as enthalpy, melting point, and boiling point. This approximation can be extended into several chemical compounds.

scholarly journals On Analysis and Computation of Degree-Based Topological Invariants for Cyclic Mesh Network

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Nida Zahra ◽  
Muhammad Ibrahim ◽  
Muhammad Kamran Siddiqui ◽  
Hajar Shooshtri
Keyword(s):  
Distributed Computing ◽  
Boiling Point ◽  
Strain Energy ◽  
Mesh Networks ◽  
Mesh Network ◽  
Topological Descriptors ◽  
Topological Invariants ◽  
Connectivity Indices ◽  
Topological Characteristics ◽  
Atom Bond

Recently, there has been increasing attention on the system network due to its promising applications in parallel hanging architectures such as distributed computing (Day (2004), Day and Al-Ayyoub (2002)). Related networks differ in the circumstances of topology, and the descriptors were freshly examined by Hayat and Imran (2014) and Hayat et al. (2014). Distance-based descriptors, counting-related descriptors, and degree-based descriptors are all examples of topological descriptors. These topological characteristics are linked to chemical features of a substance, such as stability, strain energy, and boiling point. The specifications for the 1st Zagreb alpha, 1st Zagreb beta, 2nd Zagreb, sum-connectivity, geometric-arithmetic, Randic, harmonic, and atom-bond connectivity indices for mesh networks M N m × n based on VE and EV degree are discussed in this paper.

scholarly journals Topological Indices of mth Chain Silicate Graphs

Mathematics ◽  
2019 ◽  
Vol 7 (1) ◽  
pp. 42 ◽  
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.

scholarly journals Edge-Version Atom-Bond Connectivity and Geometric Arithmetic Indices of Generalized Bridge Molecular Graphs

Symmetry ◽  
2018 ◽  
Vol 10 (12) ◽  
pp. 751 ◽  
Author(s):  
Xiujun Zhang ◽  
Xinling Wu ◽  
Shehnaz Akhter ◽  
Muhammad Jamil ◽  
Jia-Bao Liu ◽  
...  
Keyword(s):  
Molecular Graph ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Graph Invariants ◽  
Molecular Graphs ◽  
Industry Research ◽  
Chemical Graph Theory ◽  
Chain Polymerization ◽  
Definition Of ◽  
Atom Bond

Topological indices are graph invariants computed by the distance or degree of vertices of the molecular graph. In chemical graph theory, topological indices have been successfully used in describing the structures and predicting certain physicochemical properties of chemical compounds. In this paper, we propose a definition of generalized bridge molecular graphs that can model more kinds of long chain polymerization products than the bridge molecular graphs, and provide some results of the edge versions of atom-bond connectivity ( A B C e ) and geometric arithmetic ( G A e ) indices for some generalized bridge molecular graphs, which have regular, periodic and symmetrical structures. The results of this paper offer promising prospects in the applications for chemical and material engineering, especially in chemical industry research.

scholarly journals On Degree-Based Topological Indices of Symmetric Chemical Structures

Symmetry ◽  
2018 ◽  
Vol 10 (11) ◽  
pp. 619 ◽  
Author(s):  
Jia-Bao Liu ◽  
Haidar Ali ◽  
Muhammad Shafiq ◽  
Usman Munir
Keyword(s):  
Molecular Descriptor ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Chemical Compounds ◽  
Topological Indices ◽  
Chemical Structures ◽  
Physico Chemical ◽  
First Time ◽  
Ga Index ◽  
Atom Bond

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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