On Degree Based Topological Indices of TiO2 Crystal via M-Polynomial

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

Computing Topological Descriptors and Polynomials of Certain 2D Chemical Structures

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.

Study of Vanadium Carbide Structures Based on Ve and Ev-Degree Topological Indices

Vanadium is a biologically active product with significant industrial and biological applications. Vanadium is found in a variety of minerals and fossil fuels, the most common of which are sandstones, crude oil, and coal. Topological descriptors are numerical numbers assigned to the molecular structures and have the ability to predict certain of their physical/chemical properties. In this paper, we have studied topological descriptors of vanadium carbide structure based on ev and ve degrees. In particular, we have computed the closed forms of Zagreb, Randic, geometric-arithmetic, and atom-bond connectivity (ABC) indices of vanadium carbide structure based on ev and ve degrees. This kind of study may be useful for understanding the biological and chemical behavior of the structure.

Monitoring Weeder Robots and Anticipating Their Functioning by Using Advanced Topological Data Analysis

The present paper aims at analyzing the topological content of the complex trajectories that weeder-autonomous robots follow in operation. We will prove that the topological descriptors of these trajectories are affected by the robot environment as well as by the robot state, with respect to maintenance operations. Most of existing methodologies enabling efficient diagnosis are based on the data analysis, and in particular on some statistical quantities derived from the data. The present work explores the use of an original approach that instead of analyzing quantities derived from the data, analyzes the “shape” of the data, that is, the time series topology based on the homology persistence. We will prove that this procedure is able to extract valuable patterns able to discriminate the trajectories that the robot follows depending on the particular patch in which it operates, as well as to differentiate the robot behavior before and after undergoing a maintenance operation. Even if it is a preliminary work, and it does not pretend to compare its performances with respect to other existing technologies, this work opens new perspectives in considering quite natural and simple descriptors based on the intrinsic information that data contains, with the aim of performing efficient diagnosis and prognosis.

Measuring hidden phenotype: Quantifying the shape of barley seeds using the Euler Characteristic Transform

Shape plays a fundamental role in biology. Traditional phenotypic analysis methods measure some features but fail to measure the information embedded in shape comprehensively. To extract, compare, and analyze this information embedded in a robust and concise way, we turn to Topological Data Analysis (TDA), specifically the Euler Characteristic Transform. TDA measures shape comprehensively using mathematical representations based on algebraic topology features. To study its use, we compute both traditional and topological shape descriptors to quantify the morphology of 3121 barley seeds scanned with X-ray Computed Tomography (CT) technology at 127 micron resolution. The Euler Characteristic Transform measures shape by analyzing topological features of an object at thresholds across a number of directional axes. A Kruskal-Wallis analysis of the information encoded by the topological signature reveals that the Euler Characteristic Transform picks up successfully the shape of the crease and bottom of the seeds. Moreover, while traditional shape descriptors can cluster the seeds based on their accession, topological shape descriptors can cluster them further based on their panicle. We then successfully train a support vector machine (SVM) to classify 28 different accessions of barley based exclusively on the shape of their grains. We observe that combining both traditional and topological descriptors classifies barley seeds better than using just traditional descriptors alone. This improvement suggests that TDA is thus a powerful complement to traditional morphometrics to comprehensively describe a multitude of “hidden” shape nuances which are otherwise not detected.

Computation of Polynomial Degree-Based Topological Descriptors of Indu-Bala Product of Two Paths

Cheminformatics is entirely a newly coined term that encompasses a field that includes engineering computer sciences along with basic sciences. As we all know, vertices and edges form a network whereas vertex and its degrees contribute to joining edges. The degree of vertex is very much dependent on a reasonable proportion of network properties. There is no doubt that a network has to have a reliance of different kinds of hub buses, serials, and other connecting points to constitute a system that is the backbone of cheminformatics. The Indu-Bala product of two graphs G 1 and G 2 has a special notation as described in Section 2. The attainment of this product is very much due to related vertices at to different places of G 1 ∨ G 2 . This study states we have found M-polynomial and degree-based topological indices for Indu-Bala product of two paths P k and P j for j , k ≥ 2 . We also give some graphical representation of these indices and analyzed them graphically.

Closed Neighborhood Degree Sum-Based Topological Descriptors of Graphene Structures

Topological descriptors defined on chemical structures enable understanding the properties and activities of chemical molecules. In this paper, we compute closed neighborhood degree sum-based indices for four different Graphene structures. The cardinality of closed neighborhood degree-based edge partitions for four different Graphene structures is used to compute the closed neighborhood degree sum-based indices.