Localization-Delocalization Matrices and Electron Density-Weighted Adjacency/Connectivity Matrices: A Bridge Between the Quantum Theory of Atoms in Molecules and Chemical Graph Theory

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.

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Computing Topological Indices for Para-Line Graphs of Anthracene

Open Chemistry ◽

10.1515/chem-2019-0093 ◽

2019 ◽

Vol 17 (1) ◽

pp. 955-962 ◽

Cited By ~ 1

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.

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On the transferability of electron density in binary vanadium borides VB, V3B4 and VB2

Acta Crystallographica Section B Structural Science Crystal Engineering and Materials ◽

10.1107/s2052520615018363 ◽

2015 ◽

Vol 71 (6) ◽

pp. 777-787 ◽

Cited By ~ 1

Author(s):

Bürgehan Terlan ◽

Lev Akselrud ◽

Alexey I. Baranov ◽

Horst Borrmann ◽

Yuri Grin

Keyword(s):

Quantum Theory ◽

Crystal Structures ◽

Electron Density ◽

Critical Points ◽

Atoms In Molecules ◽

Model Systems ◽

Suitable Model ◽

Interatomic Distances ◽

Systematic Analysis ◽

A Charge

Binary vanadium borides are suitable model systems for a systematic analysis of the transferability concept in intermetallic compounds due to chemical intergrowth in their crystal structures. In order to underline this structural relationship, topological properties of the electron density in VB, V3B4 and VB2 reconstructed from high-resolution single-crystal X-ray diffraction data as well as derived from quantum chemical calculations, are analysed in terms of Bader's Quantum Theory of Atoms in Molecules [Bader (1990). Atoms in Molecules: A Quantum Theory, 1st ed. Oxford: Clarendon Press]. The compounds VB, V3B4 and VB2 are characterized by a charge transfer from the metal to boron together with two predominant atomic interactions, the shared covalent B—B interactions and the polar covalent B—M interactions. The resembling features of the crystal structures are well reflected by the respective B—B interatomic distances as well as by ρ(r) values at the B—B bond critical points. The latter decrease with an increase in the corresponding interatomic distances. The B—B bonds show transferable electron density properties at bond critical points depending on the respective bond distances.

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The Second Hyper-Zagreb Index of Complement Graphs and Its Applications of Some Nano Structures

Asian Journal of Probability and Statistics ◽

10.9734/ajpas/2021/v15i430364 ◽

2021 ◽

pp. 54-75

Author(s):

Mohammed Alsharafi ◽

Yusuf Zeren ◽

Abdu Alameri

Keyword(s):

Graph Theory ◽

Cartesian Product ◽

Quantitative Structure Activity Relationship ◽

Quantitative Structure ◽

Structure Property ◽

Zagreb Index ◽

Chemical Graph ◽

Strong Product ◽

Chemical Graph Theory ◽

Mathematical Operations

In chemical graph theory, a topological descriptor is a numerical quantity that is based on the chemical structure of underlying chemical compound. Topological indices play an important role in chemical graph theory especially in the quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR). In this paper, we present explicit formulae for some basic mathematical operations for the second hyper-Zagreb index of complement graph containing the join G1 + G2, tensor product G1 \(\otimes\) G2, Cartesian product G1 x G2, composition G1 \(\circ\) G2, strong product G1 * G2, disjunction G1 V G2 and symmetric difference G1 \(\oplus\) G2. Moreover, we studied the second hyper-Zagreb index for some certain important physicochemical structures such as molecular complement graphs of V-Phenylenic Nanotube V PHX[q, p], V-Phenylenic Nanotorus V PHY [m, n] and Titania Nanotubes TiO2.

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Chemical graph theory andn-center electron delocalization indices: A study on polycyclic aromatic hydrocarbons

Journal of Computational Chemistry ◽

10.1002/jcc.20647 ◽

2007 ◽

Vol 28 (10) ◽

pp. 1625-1633 ◽

Cited By ~ 29

Author(s):

Marcos Mandado ◽

María J. González-Moa ◽

Ricardo A. Mosquera

Keyword(s):

Polycyclic Aromatic Hydrocarbons ◽

Graph Theory ◽

Aromatic Hydrocarbons ◽

Electron Delocalization ◽

Chemical Graph ◽

Chemical Graph Theory ◽

Polycyclic Aromatic ◽

Electron Delocalization Indices

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Graph Applications in Chemoinformatics and Structural Bioinformatics

Advances in Data Mining and Database Management - Graph Data Management ◽

10.4018/978-1-61350-053-8.ch017 ◽

2011 ◽

pp. 386-420

Author(s):

Eleanor Joyce Gardiner

Keyword(s):

Graph Theory ◽

Molecular Graph ◽

Structural Bioinformatics ◽

Three Dimensions ◽

Chemical Graph ◽

Labeled Graph ◽

3D Space ◽

Chemical Graph Theory ◽

Computer Representation ◽

History Of

The focus of this chapter will be the uses of graph theory in chemoinformatics and in structural bioinformatics. There is a long history of chemical graph theory dating back to the 1860’s and Kekule’s structural theory. It is natural to regard the atoms of a molecule as nodes and the bonds as edges (2D representations) of a labeled graph (a molecular graph). This chapter will concentrate on the algorithms developed to exploit the computer representation of such graphs and their extensions in both two and three dimensions (where an edge represents the distance in 3D space between a pair of atoms), together with the algorithms developed to exploit them. The algorithms will generally be summarized rather than detailed. The methods were later extended to larger macromolecules (such as proteins); these will be covered in less detail.

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