scholarly journals Study of Hardness of Superhard Crystals by Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-10
Author(s):  
Xiujun Zhang ◽  
Muhammad Naeem ◽  
Abdul Qudair Baig ◽  
Manzoor Ahmad Zahid
Keyword(s):  
Molecular Structure ◽  
Chemical Structure ◽  
Topological Indices ◽  
Connectivity Index ◽  
Chemical Bonds ◽  
Randić Index ◽  
Total Resistance ◽  
Randic Index ◽  
Atom Bond

Topological indices give immense information about a molecular structure or chemical structure. The hardness of materials for the indentation can be defined microscopically as the total resistance and effect of chemical bonds in the respective materials. The aim of this paper is to study the hardness of some superhard B C x crystals by means of topological indices, specifically Randić index and atom-bond connectivity index.

scholarly journals Topological Characterization of Nanosheet Covered by C3 and C6

Processes ◽  
2019 ◽  
Vol 7 (7) ◽  
pp. 462
Author(s):  
Sumiya Nasir ◽  
Fozia Bashir Farooq ◽  
Nazeran Idrees ◽  
Muhammad Jawwad Saif ◽  
Fatima Saeed
Keyword(s):  
Chemical Structure ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Zagreb Index ◽  
Topological Characterization ◽  
Physical And Chemical ◽  
Atom Bond ◽  
And Chemical Properties

A topological index of a graph is a single numeric quantity which relates the chemical structure with its underlying physical and chemical properties. Topological indices of a nanosheet can help us to understand the properties of the material better. This study deals with computation of degree-dependent topological indices like the Randic index, first Zagreb index, second Zagreb index, geometric arithmetic index, atom bond connectivity index, sum connectivity index and hyper Zagreb index of nanosheet covered by C3 and C6. Furthermore, M-polynomial of the nanosheet is also computed, which provides an alternate way to express the topological indices.

scholarly journals Inequalities on the Generalized ABC Index

Mathematics ◽  
2021 ◽  
Vol 9 (10) ◽  
pp. 1151
Author(s):  
Paul Bosch ◽  
Edil D. Molina ◽  
José M. Rodríguez ◽  
José M. Sigarreta
Keyword(s):  
Hölder Inequality ◽  
Connectivity Index ◽  
Randić Index ◽  
Randic Index ◽  
General Randić Index ◽  
Abc Index ◽  
General Randic Index ◽  
Atom Bond

In this work, we obtained new results relating the generalized atom-bond connectivity index with the general Randić index. Some of these inequalities for ABCα improved, when α=1/2, known results on the ABC index. Moreover, in order to obtain our results, we proved a kind of converse Hölder inequality, which is interesting on its own.

scholarly journals Extremal Trees with Respect to the Difference between Atom-Bond Connectivity Index and Randić Index

Symmetry ◽  
2020 ◽  
Vol 12 (10) ◽  
pp. 1591
Author(s):  
Wan Nor Nabila Nadia Wan Zuki ◽  
Zhibin Du ◽  
Muhammad Kamran Jamil ◽  
Roslan Hasni
Keyword(s):  
Graph Theory ◽  
Connectivity Index ◽  
Randić Index ◽  
Extremal Graphs ◽  
Randic Index ◽  
Chemical Graph Theory ◽  
The Difference ◽  
Atom Bond ◽  
Chemical Trees

Let G be a simple, connected and undirected graph. The atom-bond connectivity index (ABC(G)) and Randić index (R(G)) are the two most well known topological indices. Recently, Ali and Du (2017) introduced the difference between atom-bond connectivity and Randić indices, denoted as ABC−R index. In this paper, we determine the fourth, the fifth and the sixth maximum chemical trees values of ABC−R for chemical trees, and characterize the corresponding extremal graphs. We also obtain an upper bound for ABC−R index of such trees with given number of pendant vertices. The role of symmetry has great importance in different areas of graph theory especially in chemical graph theory.

scholarly journals Topological Indices of Dendrimers used in Drug Delivery

2020 ◽  
Vol 12 (4) ◽  
pp. 645-655
Author(s):  
T. P. Jude ◽  
E. Panchadcharam ◽  
K. Masilamani
Keyword(s):  
Drug Delivery ◽  
Molecular Graph ◽  
Topological Indices ◽  
Vertex Degree ◽  
Numerical Representation ◽  
Chemical Bonds ◽  
Randić Index ◽  
Zagreb Index ◽  
Randic Index ◽  
Carrier Vehicle

The topological index is a numerical representation of a molecular structure. In chemical graphs, the atoms and the chemical bonds between them are represented by vertices and edges respectively. Vertex degree based topological indices are the most studied and mostly used type of topological indices. The mostly used vertex degree based topological indices in the field of drug design and developments are the Zagreb index and the Randić index. The structural chemistry of dendrimers could be manipulated by their topological indices to get the specific structure with required properties to deliver the drugs to target carrier vehicle. In this work, topological indices of three types of dendrimers which are used as the drug delivery system were studied and their Zagreb index and the Randić index were calculated using molecular graph theory. Moreover, the other versions of these two indices were also calculated to these dendrimers.

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 Topological Indices of Some Classes of Thorn Complete and Wheel Graphs

2021 ◽  
Vol 11 (1) ◽  
pp. 3305-3321
Keyword(s):  
Chemical Compounds ◽  
Biological Properties ◽  
Topological Indices ◽  
Randić Index ◽  
Physiochemical Properties ◽  
Randic Index ◽  
Wheel Graphs ◽  
Chemical Descriptors ◽  
Thorn Graphs ◽  
Atom Bond

We have multiple real numbers that describe chemical descriptors in the field of Graph theory. These descriptors constitute the entire structure of a graph, which possesses an actual chemical structure. Among these, the main focus of topological indices is that they are associated with many non-identical physiochemical properties of chemical compounds. Also, the biological properties of chemical compounds can be established by the topological indices. In this analysis, we compute the Reciprocal Randic index〖(R〗^(-1)), Reduced Reciprocal Randic index(〖RR〗^(-1)), Atom-bond Connectivity index(ABC) and the geometric arithmetic index(GA) of thorn graphs are obtained theoretically.

scholarly journals Degree-Based Topological Indices of Boron B12

2021 ◽  
Vol 2021 ◽  
pp. 1-6
Author(s):  
Nouman Saeed ◽  
Kai Long ◽  
Zeeshan Saleem Mufti ◽  
Hafsa Sajid ◽  
Abdul Rehman
Keyword(s):  
Chemical Structure ◽  
Chemical Reactivity ◽  
Molecular Descriptor ◽  
Topological Indices ◽  
Connectivity Index ◽  
Melting Points ◽  
Zagreb Index ◽  
Boiling Points ◽  
Electronic Parameters ◽  
Atom Bond

Topological index sometimes called molecular descriptor is a numerical value which associates a chemical composition for correlating chemical structure with numerous physical properties, chemical reactivity, or biological activity. In this paper, we study some topological indices of boron and try to correlate the physicochemical properties such as freezing points, boiling points, melting points, infrared spectrum, electronic parameters, viscosity, and density of chemical graphs. We discuss these topological indices, and some of them are mentioned here such as Randic index, the first general Zagreb index, the general sum connectivity index, hyper-Zagreb index (HM), the atom-bond connectivity index (ABC), the geometric-arithmetic index (GA), the harmonic index (H), and the forgotten index (F).

On eccentricity-based topological descriptors of water-soluble dendrimers

2018 ◽  
Vol 74 (1-2) ◽  
pp. 25-33 ◽  
Author(s):  
Zahid Iqbal ◽  
Muhammad Ishaq ◽  
Adnan Aslam ◽  
Wei Gao
Keyword(s):  
Molecular Structure ◽  
Chemical Properties ◽  
Topological Indices ◽  
Water Soluble ◽  
Connectivity Index ◽  
Topological Descriptors ◽  
Physical And Chemical Properties ◽  
Eccentric Connectivity Index ◽  
Physical And Chemical ◽  
And Chemical Properties

AbstractPrevious studies show that certain physical and chemical properties of chemical compounds are closely related with their molecular structure. As a theoretical basis, it provides a new way of thinking by analyzing the molecular structure of the compounds to understand their physical and chemical properties. The molecular topological indices are numerical invariants of a molecular graph and are useful to predict their bioactivity. Among these topological indices, the eccentric-connectivity index has a prominent place, because of its high degree of predictability of pharmaceutical properties. In this article, we compute the closed formulae of eccentric-connectivity–based indices and its corresponding polynomial for water-soluble perylenediimides-cored polyglycerol dendrimers. Furthermore, the edge version of eccentric-connectivity index for a new class of dendrimers is determined. The conclusions we obtained in this article illustrate the promising application prospects in the field of bioinformatics and nanomaterial engineering.

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