molecular graph
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2022 ◽  
Vol 19 (2) ◽  
pp. 2022
Author(s):  
Tapan Kumar Baishya ◽  
Bijit Bora ◽  
Pawan Chetri ◽  
Upashana Gogoi

Topological indices (TI) (descriptors) of a molecular graph are very much useful to study various physiochemical properties. It is also used to develop the quantitative structure-activity relationship (QSAR), quantitative structure-property relationship (QSPR) of the corresponding chemical compound. Various techniques have been developed to calculate the TI of a graph. Recently a technique of calculating degree-based TI from M-polynomial has been introduced. We have evaluated various topological descriptors for 3-dimensional TiO2 crystals using M-polynomial. These descriptors are constructed such that it contains 3 variables (m, n and t) each corresponding to a particular direction. These 3 variables facilitate us to deeply understand the growth of TiO2 in 1 dimension (1D), 2 dimensions (2D), and 3 dimensions (3D) respectively. HIGHLIGHTS Calculated degree based Topological indices of a 3D crystal from M-polynomial A relation among various Topological indices is established geometrically Variations of Topological Indices along three dimensions (directions) are shown geometrically Harmonic index approximates the degree variation of oxygen atom


2022 ◽  
Author(s):  
Takahiro Inoue ◽  
Kenichi Tanaka ◽  
Kimito Funatsu
Keyword(s):  

2021 ◽  
Vol 2021 ◽  
pp. 1-16
Author(s):  
Muhammad Mubashir Izhar ◽  
Zahida Perveen ◽  
Dalal Alrowaili ◽  
Mehran Azeem ◽  
Imran Siddique ◽  
...  

In the fields of mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are an analytical framework of a graph which portray its topology and are mostly equal graphs. Topological indices (TIs) are numeral quantities that are used to foresee the natural correlation among the physicochemical properties of the chemical compounds in their fundamental network. TIs show an essential role in the theoretical abstract and environmental chemistry and pharmacology. In this paper, we compute many latest developed degree-based TIs. An analogy among the computed different versions of the TIs with the help of the numerical values and their graphs is also included .In this article, we compute the first Zagreb index, second Zagreb index, hyper Zagreb index, ABC Index, GA Index, and first Zagreb polynomial and second Zagreb polynomial of chemical graphs polythiophene, nylon 6,6, and the backbone structure of DNA.


2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Aqsa Sattar ◽  
Muhammad Javaid ◽  
Ebenezer Bonyah

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.


2021 ◽  
Vol 2021 ◽  
pp. 1-15
Author(s):  
Weidong Zhao ◽  
K. Julietraja ◽  
P. Venugopal ◽  
Xiujun Zhang

Theoretical chemists are fascinated by polycyclic aromatic hydrocarbons (PAHs) because of their unique electromagnetic and other significant properties, such as superaromaticity. The study of PAHs has been steadily increasing because of their wide-ranging applications in several fields, like steel manufacturing, shale oil extraction, coal gasification, production of coke, tar distillation, and nanosciences. Topological indices (TIs) are numerical quantities that give a mathematical expression for the chemical structures. They are useful and cost-effective tools for predicting the properties of chemical compounds theoretically. Entropic network measures are a type of TIs with a broad array of applications, involving quantitative characterization of molecular structures and the investigation of some specific chemical properties of molecular graphs. Irregularity indices are numerical parameters that quantify the irregularity of a molecular graph and are used to predict some of the chemical properties, including boiling points, resistance, enthalpy of vaporization, entropy, melting points, and toxicity. This study aims to determine analytical expressions for the VDB entropy and irregularity-based indices in the rectangular Kekulene system.


2021 ◽  
Vol 11 (24) ◽  
pp. 11696
Author(s):  
Patrick W. Fowler ◽  
Barry T. Pickup

A fully analytical model is presented for ballistic conduction in a multi-lead device that is based on a π-conjugated carbon framework attached to a single source lead and several sink leads. This source-and-multiple-sink potential (SMSP) model is rooted in the Ernzerhof source-and-sink potential (SSP) approach and specifies transmission in terms of combinations of structural polynomials based on the molecular graph. The simplicity of the model allows insight into many-lead devices in terms of constituent two-lead devices, description of conduction in the multi-lead device in terms of structural polynomials, molecular orbital channels, and selection rules for active and inert leads and orbitals. In the wide-band limit, transmission can be expressed entirely in terms of characteristic polynomials of vertex-deleted graphs. As limiting cases of maximum connection, complete symmetric devices (CSD) and complete bipartite symmetric devices (CBSD) are defined and solved analytically. These devices have vanishing lead-lead interference effects. Illustrative calculations of transmission curves for model small-molecule systems are presented and selection rules are identified.


2021 ◽  
Author(s):  
Yingheng Wang ◽  
Yaosen Min ◽  
Erzhuo Shao ◽  
Ji Wu
Keyword(s):  

2021 ◽  
Author(s):  
Yingheng Wang ◽  
Yaosen Min ◽  
Erzhuo Shao ◽  
Ji Wu

ABSTRACTLearning generalizable, transferable, and robust representations for molecule data has always been a challenge. The recent success of contrastive learning (CL) for self-supervised graph representation learning provides a novel perspective to learn molecule representations. The most prevailing graph CL framework is to maximize the agreement of representations in different augmented graph views. However, existing graph CL frameworks usually adopt stochastic augmentations or schemes according to pre-defined rules on the input graph to obtain different graph views in various scales (e.g. node, edge, and subgraph), which may destroy topological semantemes and domain prior in molecule data, leading to suboptimal performance. Therefore, designing parameterized, learnable, and explainable augmentation is quite necessary for molecular graph contrastive learning. A well-designed parameterized augmentation scheme can preserve chemically meaningful structural information and intrinsically essential attributes for molecule graphs, which helps to learn representations that are insensitive to perturbation on unimportant atoms and bonds. In this paper, we propose a novel Molecular Graph Contrastive Learning with Parameterized Explainable Augmentations, MolCLE for brevity, that self-adaptively incorporates chemically significative information from both topological and semantic aspects of molecular graphs. Specifically, we apply deep neural networks to parameterize the augmentation process for both the molecular graph topology and atom attributes, to highlight contributive molecular substructures and recognize underlying chemical semantemes. Comprehensive experiments on a variety of real-world datasets demonstrate that our proposed method consistently outperforms compared baselines, which verifies the effectiveness of the proposed framework. Detailedly, our self-supervised MolCLE model surpasses many supervised counterparts, and meanwhile only uses hundreds of thousands of parameters to achieve comparative results against the state-of-the-art baseline, which has tens of millions of parameters. We also provide detailed case studies to validate the explainability of augmented graph views.CCS CONCEPTS• Mathematics of computing → Graph algorithms; • Applied computing → Bioinformatics; • Computing methodologies → Neural networks; Unsupervised learning.


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