scholarly journals Topological Indices of Pent-Heptagonal Nanosheets via M-Polynomials

2021 ◽  
Vol 2021 ◽  
pp. 1-13
Author(s):  
Hafiza Bushra Mumtaz ◽  
Muhammad Javaid ◽  
Hafiz Muhammad Awais ◽  
Ebenezer Bonyah
Keyword(s):  
Physical Chemistry ◽  
Graph Theory ◽  
Biological Properties ◽  
Topological Indices ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Engineering And Technology ◽  
Different Types ◽  
Mathematical Sciences ◽  
And Mathematics

The combination of mathematical sciences, physical chemistry, and information sciences leads to a modern field known as cheminformatics. It shows a mathematical relationship between a property and structural attributes of different types of chemicals called quantitative-structures’ activity and qualitative-structures’ property relationships that are utilized to forecast the chemical sciences and biological properties, in the field of engineering and technology. Graph theory has originated a significant usage in the field of physical chemistry and mathematics that is famous as chemical graph theory. The computing of topological indices (TIs) is a new topic of chemical graphs that associates many physiochemical characteristics of the fundamental organic compounds. In this paper, we used the M-polynomial-based TIs such as 1st Zagreb, 2nd Zagreb, modified 2nd Zagreb, symmetric division deg, general Randi c ´ , inverse sum, harmonic, and augmented indices to study the chemical structures of pent-heptagonal nanosheets of V C 5 C 7 and H C 5 C 7 . An estimation among the computed TIs with the help of numerical results is also presented.

scholarly journals M-Polynomials and Degree-Based Topological Indices of Triangular, Hourglass, and Jagged-Rectangle Benzenoid Systems

2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Young Chel Kwun ◽  
Ashaq Ali ◽  
Waqas Nazeer ◽  
Maqbool Ahmad Chaudhary ◽  
Shin Min Kang
Keyword(s):  
Graph Theory ◽  
Biological Properties ◽  
Vital Role ◽  
Topological Indices ◽  
Molecular Topology ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Research Fields ◽  
Chemical Graph Theory ◽  
Active Research

Chemical graph theory is a branch of mathematical chemistry which has an important effect on the development of the chemical sciences. The study of topological indices is currently one of the most active research fields in chemical graph theory. Topological indices help to predict many chemical and biological properties of chemical structures under study. The aim of this report is to study the molecular topology of some benzenoid systems. M-polynomial has wealth of information about the degree-based topological indices. We compute M-polynomials for triangular, hourglass, and jagged-rectangle benzenoid systems, and from these M-polynomials, we recover nine degree-based topological indices. Our results play a vital role in pharmacy, drug design, and many other applied areas.

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 ve-degree- and ev-degree-based topological properties of crystallographic structure of cuprite Cu2O

2021 ◽  
Vol 19 (1) ◽  
pp. 576-585
Author(s):  
Shu-Bo Chen ◽  
Abdul Rauf ◽  
Muhammad Ishtiaq ◽  
Muhammad Naeem ◽  
Adnan Aslam
Keyword(s):  
Graph Theory ◽  
Copper Oxide ◽  
Topological Indices ◽  
Topological Descriptors ◽  
Crystallographic Structure ◽  
Chemical Substances ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Enormous Number

Abstract In the study of chemical graph theory, an enormous number of research analyses have confirmed that the characteristics of chemicals have a nearby connection with their atomic structure. Topological indices were the critical tools for the analysis of these chemical substances to consider the essential topology of chemical structures. Topological descriptors are the significant numerical quantities or invariant in the fields of chemical graph theory. In this study, we have studied the crystal structure of copper oxide ( Cu 2 O {{\rm{Cu}}}_{2}{\rm{O}} ) chemical graph, and further, we have calculated the ev-degree- and ve-degree-based topological indices of copper oxide chemical graph. This kind of study may be useful for understanding the atomic mechanisms of corrosion and stress–corrosion cracking of copper.

scholarly journals Multiplicative topological indices of honeycomb derived networks

Open Physics ◽  
2019 ◽  
Vol 17 (1) ◽  
pp. 16-30
Author(s):  
Jiang-Hua Tang ◽  
Mustafa Habib ◽  
Muhammad Younas ◽  
Muhammad Yousaf ◽  
Waqas Nazeer
Keyword(s):  
Graph Theory ◽  
Structural Properties ◽  
Chemical Properties ◽  
Vital Role ◽  
Topological Indices ◽  
Chemical Graph ◽  
Chemical Structures ◽  
Chemical Graph Theory ◽  
Physico Chemical

Abstract Topological indices are the numerical values associated with chemical structures that correlate physico-chemical properties with structural properties. There are various classes of topological indices such as degree based topological indices, distance based topological indices and counting related topological indices. Among these classes, degree based topological indices are of great importance and play a vital role in chemical graph theory, particularly in chemistry. In this report, we have computed the multiplicative degree based topological indices of honeycomb derived networks of dimensions I, 2, 3 and 4.

scholarly journals Connection-Based Multiplicative Zagreb Indices of Dendrimer Nanostars

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aqsa Sattar ◽  
Muhammad Javaid ◽  
Ebenezer Bonyah
Keyword(s):  
Graph Theory ◽  
Physicochemical Properties ◽  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
Zagreb Indices ◽  
Mathematical Chemistry ◽  
Chemical Structures ◽  
And Mathematics

The field of graph theory is broadly growing and playing a remarkable role in cheminformatics, mainly in chemistry and mathematics in developing different chemical structures and their physicochemical properties. Mathematical chemistry provides a platform to study these physicochemical properties with the help of topological indices (TIs). A topological index (TI) is a function that connects a numeric number to each molecular graph. Zagreb indices (ZIs) are the most studied TIs. In this paper, we establish general expressions to calculate the connection-based multiplicative ZIs, namely, first multiplicative ZIs, second multiplicative ZIs, third multiplicative ZIs, and fourth multiplicative ZIs, of two renowned dendrimer nanostars. The defined expressions just depend on the step of growth of these dendrimers. Moreover, we have compared our calculated for both type of dendrimers with each other.

WEIGHTED MOSTAR INDICES OF CERTAIN GRAPHS

2021 ◽  
Vol 10 (9) ◽  
pp. 3093-3111
Author(s):  
P. Kandan ◽  
S. Subramanian ◽  
P. Rajesh
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Molecular Graph ◽  
Topological Indices ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
And Mathematics

Chemical graph theory is a mixture of chemistry and mathematics both play an important role in chemical graph theory. Chemistry provides a chemical compound and graph theory transform this chemical compound into a molecular graph, which are associated with some numerical values these values are known as topological indices. In this study we consider the weighted modification of new bond-additive Mostar indices that appear to provide quantitative measures of peripheral shapes of molecules. We have computed the Additively Weighted Mostar Index and Multiplicatively Weighted Mostar Index for Conical and Generalized gear graph.

scholarly journals M-polynomial and topological indices of zigzag edge coronoid fused by starphene

2020 ◽  
Vol 18 (1) ◽  
pp. 1362-1369
Author(s):  
Farkhanda Afzal ◽  
Sabir Hussain ◽  
Deeba Afzal ◽  
Saira Hameed
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Zigzag Edge ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Chemical Graphs

AbstractChemical graph theory is a subfield of graph theory that studies the topological indices for chemical graphs that have a good correlation with chemical properties of a chemical molecule. In this study, we have computed M-polynomial of zigzag edge coronoid fused by starphene. We also investigate various topological indices related to this graph by using their M-polynomial.

scholarly journals Computing Topological Indices for Para-Line Graphs of Anthracene

2019 ◽  
Vol 17 (1) ◽  
pp. 955-962 ◽  
Author(s):  
Zhiqiang Zhang ◽  
Zeshan Saleem Mufti ◽  
Muhammad Faisal Nadeem ◽  
Zaheer Ahmad ◽  
Muhammad Kamran Siddiqui ◽  
...  
Keyword(s):  
Graph Theory ◽  
Chemical Compound ◽  
Line Graph ◽  
Molecular Graph ◽  
Chemical Properties ◽  
Molar Refraction ◽  
Chromatographic Behavior ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
And Mathematics

AbstractAtoms displayed as vertices and bonds can be shown by edges on a molecular graph. For such graphs we can find the indices showing their bioactivity as well as their physio-chemical properties such as the molar refraction, molar volume, chromatographic behavior, heat of atomization, heat of vaporization, magnetic susceptibility, and the partition coefficient. Today, industry is flourishing because of the interdisciplinary study of different disciplines. This provides a way to understand the application of different disciplines. Chemical graph theory is a mixture of chemistry and mathematics, which plays an important role in chemical graph theory. Chemistry provides a chemical compound, and graph theory transforms this chemical compound into a molecular graphwhich further is studied by different aspects such as topological indices.We will investigate some indices of the line graph of the subdivided graph (para-line graph) of linear-[s] Anthracene and multiple Anthracene.

scholarly journals Molecular Properties of Carbon Crystal Cubic Structures

2020 ◽  
Vol 18 (1) ◽  
pp. 339-346 ◽  
Author(s):  
Hong Yang ◽  
Muhammad Kamran Siddiqui ◽  
Muhammad Naeem ◽  
Najma Abdul Rehman
Keyword(s):  
Graph Theory ◽  
Line Segment ◽  
Topological Indices ◽  
Molecular Properties ◽  
Chemical Graph ◽  
Atomic Properties ◽  
Chemical Graph Theory ◽  
Chemical Graphs ◽  
Graphical Structure ◽  
Carbon Crystal

AbstractGraph theory assumes an imperative part in displaying and planning any synthetic structure or substance organizer. Chemical graph theory facilitates in conception of the chemical graphs for their atomic properties. The graphical structure of a chemical involves atoms termed as vertices and the line segment between two different vertices are called edges. In this manuscript, our concentration is on the chemical graph of carbon graphite and cubic carbon. Additionally, we also define a procedure and calculate the degree based topological indices namely Zagreb type indices, Balaban, Forgotten and Augmented indices.

scholarly journals On Some Ve-Degree and Harmonic Molecular Topological Properties of Carborundum

2020 ◽  
Vol 8 (1) ◽  
pp. 65
Author(s):  
Murat Cancan ◽  
Kerem Yamaç ◽  
Ziyattin Taş ◽  
Mehmet Şerif Aldemir
Keyword(s):  
Silicon Carbide ◽  
Graph Theory ◽  
Topological Indices ◽  
Topological Properties ◽  
Degree Sum ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Degree Harmonic ◽  
Atom Bond

Carborundum, also known as silicon carbide which containing carbon and silicon, is a semiconductor. Molecular topological properties of physical substances are important tools to investigate the underlying topology of these substances. Ev-degree and ve-degree based on the molecular topological indices have been defined as parallel to their corresponding classical degree based topological indices in chemical graph theory. Classical degree based topological properties of carborundum have been investigated recently. As a continuation of these studies, in this study, we compute novel ve-degree harmonic, ve-degree sum-connectivity, ve-degree geometric-arithmetic, and ve-degree atom-bond connectivity, the first and the fifth harmonic molecular topological indices of two carborundum structures. 

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