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

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.

2020 ◽  
Vol 18 (1) ◽  
pp. 1362-1369
Author(s):  
Farkhanda Afzal ◽  
Sabir Hussain ◽  
Deeba Afzal ◽  
Saira Hameed

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.


2021 ◽  
Vol 33 (4) ◽  
pp. 30-41
Author(s):  
V.R. KULLI ◽  
◽  
B. CHALUVARAJU ◽  
T.V. ASHA ◽  
◽  
...  

Chemical graph theory is a branch of graph theory whose focus of interest is to finding topological indices of chemical graphs which correlate well with chemical properties of the chemical molecules. In this paper, we compute the Nirmala index, first and second inverse Nirmala indices for some chemical networks like silicate networks, chain silicate networks, hexagonal networks, oxide networks and honeycomb networks along with their comparative analysis.


Author(s):  
Wei Gao ◽  
Waqas Nazeer ◽  
Amna Yousaf ◽  
Shin Min Kang

Graph theory plays a crucial role in modeling and designing of chemical structure or chemical network. Chemical Graph theory helps to understand the molecular structure of molecular graph. The molecular graph consists of atoms as vertices and bonds as edges. Topological indices capture symmetry of molecular structures and give it a mathematical language to predict properties such as boiling points, viscosity, the radius of gyrations etc. In this article, we study the chemical graph of carbon Crystal structure of graphite and cubic carbon and compute several degree-based topological indices. Firstly we compute M-Polynomials of these structures and then from these M-polynomials we recover nine degree-based topological indices.


2020 ◽  
Vol 8 (1) ◽  
pp. 65
Author(s):  
Murat Cancan ◽  
Kerem Yamaç ◽  
Ziyattin Taş ◽  
Mehmet Şerif Aldemir

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. 


2018 ◽  
Vol 26 (1) ◽  
pp. 91-104 ◽  
Author(s):  
Prosanta Sarkar ◽  
Nilanjan De ◽  
Anita Pal

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.


2018 ◽  
Vol 2018 ◽  
pp. 1-8 ◽  
Author(s):  
Young Chel Kwun ◽  
Ashaq Ali ◽  
Waqas Nazeer ◽  
Maqbool Ahmad Chaudhary ◽  
Shin Min Kang

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.


2016 ◽  
Vol 2016 ◽  
pp. 1-5 ◽  
Author(s):  
Nilanjan De

Titania nanotube is a well-known semiconductor and has numerous technological applications. In chemical graph theory, topological indices provide an important tool to quantify the molecular structure and it is found that there is a strong correlation between the properties of chemical compounds and their molecular structure. Among different topological indices, degree-based topological indices are most studied and have some important applications. In this study, several old and new degree-based topological indices have been investigated for titania TiO2 nanotubes.


Author(s):  
Xiaona Fang ◽  
Lihua You ◽  
Hechao Liu

Hexagonal chains are a special class of catacondensed benzenoid system and phenylene chains are a class of polycyclic aromatic compounds. Recently, A family of Sombor indices was introduced by Gutman in the chemical graph theory. It had been examined that these indices may be successfully applied on modeling thermodynamic properties of compounds. In this paper, we study the expected values of the Sombor indices in random hexagonal chains, phenylene chains, and consider the Sombor indices of some chemical graphs such as graphene, coronoid systems and carbon nanocones.


Symmetry ◽  
2020 ◽  
Vol 12 (6) ◽  
pp. 932 ◽  
Author(s):  
Santanu Acharjee ◽  
Bijit Bora ◽  
Robin I. M. Dunbar

Topological indices describe mathematical invariants of molecules in mathematical chemistry. M-polynomials of chemical graph theory have freedom about the nature of molecular graphs and they play a role as another topological invariant. Social networks can be both cyclic and acyclic in nature. We develop a novel application of M-polynomials, the ( m , n , r ) -agent recruitment graph where n > 1 , to study the relationship between the Dunbar graphs of social networks and the small-world phenomenon. We show that the small-world effects are only possible if everyone uses the full range of their network when selecting steps in the small-world chain. Topological indices may provide valuable insights into the structure and dynamics of social network graphs because they incorporate an important element of the dynamical transitivity of such graphs.


2021 ◽  
Vol 19 (1) ◽  
pp. 646-652
Author(s):  
Dongming Zhao ◽  
Manzoor Ahmad Zahid ◽  
Rida Irfan ◽  
Misbah Arshad ◽  
Asfand Fahad ◽  
...  

Abstract In recent years, several structure-based properties of the molecular graphs are understood through the chemical graph theory. The molecular graph G G of a molecule consists of vertices and edges, where vertices represent the atoms in a molecule and edges represent the chemical bonds between these atoms. A numerical quantity that gives information related to the topology of the molecular graphs is called a topological index. Several topological indices, contributing to chemical graph theory, have been defined and vastly studied. Recent inclusions in the class of the topological indices are the K-Banhatti indices. In this paper, we established the precise formulas for the first and second K-Banhatti, modified K-Banhatti, K-hyper Banhatti, and hyper Revan indices of silicon carbide Si 2 C 3 {{\rm{Si}}}_{2}{{\rm{C}}}_{3} - III [ n , m ] {\rm{III}}\left[n,m] . In addition, we present the graphical analysis along with the comparison of these indices for Si 2 C 3 {{\rm{Si}}}_{2}{{\rm{C}}}_{3} - III [ n , m ] {\rm{III}}\left[n,m] .


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