scholarly journals Vibration-based biomimetic odor classification

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Nidhi Pandey ◽  
Debasattam Pal ◽  
Dipankar Saha ◽  
Swaroop Ganguly
Keyword(s):  
Spectral Clustering ◽  
Atomistic Simulations ◽  
Vibrational Modes ◽  
Shape Theory ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Eigen Value ◽  
Odorant Molecule ◽  
Physical Insight ◽  
Odor Classification

AbstractOlfaction is not as well-understood as vision or audition, nor technologically addressed. Here, Chemical Graph Theory is shown to connect the vibrational spectrum of an odorant molecule, invoked in the Vibration Theory of Olfaction, to its structure, which is germane to the orthodox Shape Theory. Atomistic simulations yield the Eigen-VAlue (EVA) vibrational pseudo-spectra for 20 odorant molecules grouped into 6 different ‘perceptual’ classes by odour. The EVA is decomposed into peaks corresponding to different types of vibrational modes. A novel secondary pseudo-spectrum, informed by this physical insight—the Peak-Decomposed EVA (PD-EVA)—has been proposed here. Unsupervised Machine Learning (spectral clustering), applied to the PD-EVA, clusters the odours into different ‘physical’ (vibrational) classes that match the ‘perceptual’, and also reveal inherent perceptual subclasses. This establishes a physical basis for vibration-based odour classification, harmonizes the Shape and Vibration theories, and points to vibration-based sensing as a promising path towards a biomimetic electronic nose.

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 Eccentricity based topological indices of face centered cubic lattice FCC(n)

2020 ◽  
Vol 44 (1) ◽  
pp. 32-38
Author(s):  
Hani Shaker ◽  
Muhammad Imran ◽  
Wasim Sajjad
Keyword(s):  
Wiener Index ◽  
Face Centered Cubic ◽  
Eccentric Connectivity Index ◽  
Zagreb Index ◽  
Cubic Lattice ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Wide Range ◽  
Unit Cells ◽  
Face Centered

Abstract Chemical graph theory has become a prime gadget for mathematical chemistry due to its wide range of graph theoretical applications for solving molecular problems. A numerical quantity is named as topological index which explains the topological characteristics of a chemical graph. Recently face centered cubic lattice FCC(n) attracted large attention due to its prominent and distinguished properties. Mujahed and Nagy (2016, 2018) calculated the precise expression for Wiener index and hyper-Wiener index on rows of unit cells of FCC(n). In this paper, we present the ECI (eccentric-connectivity index), TCI (total-eccentricity index), CEI (connective eccentric index), and first eccentric Zagreb index of face centered cubic lattice.

Atomistic Simulations of Vibrational Modes of Crystalline Nanoinclusions in an Amorphous Matrix

2017 ◽  
pp. 207-236
Author(s):  
Tanguy Damart ◽  
Yaroslav M. Beltukov ◽  
Amani Tlili ◽  
Anne Tanguy
Keyword(s):  
Amorphous Matrix ◽  
Atomistic Simulations ◽  
Vibrational Modes

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

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.

Graph Applications in Chemoinformatics and Structural Bioinformatics

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.

Chemical Graph Theory

2008 ◽  
Author(s):  
Kimberly Jordan Burch
Keyword(s):  
Graph Theory ◽  
Chemical Graph ◽  
Chemical Graph Theory

scholarly journals Hosoya and Harary Polynomials of TOX(n),RTOX(n),TSL(n) and RTSL(n)

2019 ◽  
Vol 2019 ◽  
pp. 1-18 ◽  
Author(s):  
Lian Chen ◽  
Abid Mehboob ◽  
Haseeb Ahmad ◽  
Waqas Nazeer ◽  
Muhammad Hussain ◽  
...  
Keyword(s):  
Topological Index ◽  
Molecular Descriptor ◽  
Wiener Index ◽  
Vital Role ◽  
Harary Index ◽  
Chemical Graph ◽  
Chemical Graph Theory ◽  
Hosoya Polynomial ◽  
Molecular Branching ◽  
Path Number

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. In 1947, Wiener introduced “path number” which is now known as Wiener index and is the oldest topological index related to molecular branching. Hosoya polynomial plays a vital role in determining Wiener index. In this report, we computed the Hosoya and the Harary polynomials for TOX(n),RTOX(n),TSL(n), and RTSL(n) networks. Moreover, we computed serval distance based topological indices, for example, Wiener index, Harary index, and multiplicative version of wiener index.

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