Randic Index Research Articles

On Multiplicative Sum connectivity index, Multiplicative Randic index and Multiplicative Harmonic index of some Nanostar Dendrimers

On Multiplicative Sum connectivity index, Multiplicative Randic index and Multiplicative Harmonic index of some Nanostar Dendrimers

Topological Characterization of the Symmetrical Structure of Bismuth Tri-Iodide

The bismuth tri-iodide ( B i I 3 ) is an inorganic compound. It is the result of the response of bismuth and iodine, which has inspired enthusiasm for subjective inorganic investigation. The topological indices are the numerical invariants of the molecular graph that portray its topology and are normally graph invariants. In 1975, Randic presented, in a bond-added substance, a topological index as a descriptor for portraying subatomic branching. In this paper, we investigate the precious stone structure of bismuth tri-iodide chain and sheet. Moreover, exact formulas of degree-based added-substance topological indices principally the first, second, and hyper Zagreb indices, the general Randic index, the geometric-arithmetic index, the fourth atom-bond connectivity index, and the fifth geometric arithmetic index of the subatomic graph of bismuth tri-iodide for both chain and sheet structures are determined.

M-Polynomials and Topological Indices of Dominating David Derived Networks

Abstract There is a strong relationship between the chemical characteristics of chemical compounds and their molecular structures. Topological indices are numerical values associated with the chemical molecular graphs that help to understand the physical features, chemical reactivity, and biological activity of chemical compound. Thus, the study of the topological indices is important. M-polynomial helps to recover many degree-based topological indices for example Zagreb indices, Randic index, symmetric division idex, inverse sum index etc. In this article we compute M-polynomials of dominating David derived networks of the first type, second type and third type of dimension n and find some topological properties by using these M-polynomials. The results are plotted using Maple to see the dependence of topological indices on the involved parameters.

Relationship between Standard Enthalpies/Entropies of Formation and Topological Structural Characteristics for Saturated Hydrocarbons

QSPR models are proposed that satisfactorily describe the relationships between standard enthalpies/ entropies of formation and topological indices in the form of Wiener and Randic indices and the sum of the squares of the eigenvalues from the adjacency matrix of a molecular graph. The models can be recommended for use in scientific and engineering calculations of thermodynamic functions.

More results on extremum Randic indices of (molecular) trees

The Randic index R(G) of a graph G is the sum of the weights (dudv)-1/2 of all edges uv in G, where du denotes the degree of vertex u. Du and Zhou [On Randic indices of trees, unicyclic graphs, and bicyclic graphs, Int. J. Quantum Chem. 111 (2011), 2760-2770] determined the n-vertex trees with the third for n ? 7, the fourth for n ? 10, the fifth and the sixth for n ? 11 maximum Randic indices. Recently, Li et al. [The Randic indices of trees, unicyclic graphs and bicyclic graphs, Ars Comb. 127 (2016), 409-419] obtained the n-vertex trees with the seventh, the eighth, the ninth and the tenth for n ? 11 maximum Randic indices. In this paper, we correct the ordering for the Randic indices of trees obtained by Li et al., and characterize the trees with from the seventh to the sixteenth maximum Randic indices. The obtained extremal trees are molecular and thereby the obtained ordering also holds for molecular trees.

More on inverse degree and topological indices of graphs

The inverse degree of a graph G with no isolated vertices is defined as the sum of reciprocal of vertex degrees of the graph G. In this paper, we obtain several lower and upper bounds on inverse degree ID(G). Moreover, using computational results, we prove our upper bound is strong and has the smallest deviation from the inverse degree ID(G). Next, we compare inverse degree ID(G) with topological indices (Randic index R(G), geometric-arithmetic index GA(G)) for chemical trees and also we determine the n-vertex chemical trees with the minimum, the second and the third minimum, as well as the second and the third maximum of ID - R. In addition, we correct the second and third minimum Randic index chemical trees in [16].

On certain topological indices of octahedral and icosahedral networks

The authors have computed topological indices of two metal-organic frameworks of considerable interest in reticular chemistry, namely octahedral and icosahedral networks. The topological indices of these metal-organic frameworks are extremely useful not only in the characterisation of these complex networks but also in obtaining correlation relationships of a number of their properties. In this study, they have obtained exact analytical expressions for a large number of topological indices such as the Randic index, Zagreb index, harmonic index, sum-connectivity index, atom-bond connectivity index, geometric-arithmetic index and their corresponding variants for the two newly constructed networks. Furthermore, they have used the recently introduced partition method by the transitive closure of Djokovic-Winkler relation to obtain the Wiener indices for the chain and even cyclic octahedral and icosahedral frameworks with an observation that this method is not successful in computing the Wiener index of these two networks and they pose an open problem for the same.

On ve-degree molecular topological properties of silicate and oxygen networks

Silicate based inorganic materials are important for the synthesis of a new inorganic molecules in which the studies for ultrahigh proton conductivity and catalysis. Quantitative structure-property and structure-activity relationships of the silicate oxygen networks necessitate expressions for the molecular topological features of these networks. In QSPR/QSAR studies, physicochemical characteristics and molecular topological indices such as atom-bond connectivity (ABC), geometric-arithmetic (GA), harmonic (H) and sum-connectivity (χ) indices are used to model the physicochemical properties of chemical compounds and networks. These topological indices are based on the degrees of the vertices (atoms) of a connected graph. Recently, two novel degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study by using the ve-degree concept, we define ve-degree atom-bond connectivity (ve-ABC), ve-degree geometric-arithmetic (ve-GA), ve-degree harmonic (ve-H) and ve-degree sum-connectivity (ve-χ) indices as parallel to their corresponding classical degree versions. We show that the ve-degree sum-connectivity index give better correlation than Wiener, Zagreb and Randic indices to predict the acentric factor of octanes. Also, we compute the ve-degree topological indices for some silicate oxygen netwoks such as dominating oxide network (DOX), regular triangulene oxide network (RTOX), dominating silicate network (DSL) and derive analytical closed formulae of these networks.

Estimating Graph Robustness Through the Randic Index.

Graph robustness-the ability of a graph to preserve its connectivity after the loss of nodes and edges-has been extensively studied to quantify how social, biological, physical, and technical systems withstand to external damages. In this paper, we prove that graph robustness can be quickly estimated through the Randic index, a parameter introduced in chemistry to study organic compounds. We prove that Erdos-Renyj (ER) graphs are a good specimen of robust graphs because they lack of a clear modular structure; we derive an analytical expression for the Randic index of ER graphs and use ER graphs as an effective term of comparison to decide about graph robustness. Experiments on real datasets from different domains (scientific collaboration networks, content-sharing systems, co-purchase networks from an e-commerce platform, and a road network) show that real-life large graphs are more robust than ER ones with the same number of nodes and edges. We also observe that if node degree distribution closely follows a power law, then few edges contribute for more than half of the Randic index, thus indicating that the selective removal of those edges has devastating impact on graph robustness. Finally, we describe sampling-based algorithms to efficiently but accurately approximate the Randic index.

Investigation on Tri-hexagonal Boron Nanotube by Exploiting the Certain Topological Indices and Their <i>M</i><i>-</i>polynomials

Due to the presence of multicenter bonds and their novel electronic properties, boron nanotubes are attractive. The tri-hexagonal boron nanotubes are build up from triangles and hexagons. It is useful to the QSPR/QSAR studies. Topological indices are classified in different forms such as, degree based topological indices, distance based topological indices and counting related topological indices etc. Here, we concentrated the reckoning of topological indices such as first zagreb, second zagreb, modified second zagreb index, generalized randic index, symmetric division degree index for the tri-hexagonal boron nanotube. Also, established their M-polynomials and using maple software plotted the 3D structure.

Relationship between the structure and physicochemical characteristics of 1,2,3,4-tetrahydroquinoline derivatives

A number of physicochemical characteristics of ten 1,2,3,4-tetrahydroquinoline derivatives synthesized for the first time, along with their third order Wiener and Randic indices are calculated by quantum chemical methods. Correlations between the topological indices, physicochemical parameters, and retention factors of the mentioned compounds are obtained for conditions of reversed-phase high performance liquid chromatography on porous graphitized carbon.

Prediction of changes in the heat capacity of the liquid–vapor phase transition based on modified Randič indices. Alkanes and oxygen-containing compounds

The work proposes a method to predict changes in the heat capacity of the liquid—vapor phase transition Δ l g Ср 0 (298.2) based on modified Randic indices for alkanes and acyclic oxygen-containing compounds: alcohols, aldehydes, ketones, ethers, and esters. Based on the obtained Δ l g Ср 0 (298.2) values heat capacities in the liquid phase Cp liq 0 (298.2) are calculated for the compounds under study.

Four Vertex-Degree-Based Topological Indices of VC\(_5\)C\(_7[p;q]\) Nanotubes

Recently, I. Gutman et al. presented four vertex-degree based graph invariants, that earlier have been considered in the chemical and/or mathematical literature, but, that evaded the attention of most mathematical chemists. These are the reciprocal Randic index (RR), the reduced reciprocal Randic index (RRR), the reduced second Zagreb index (RM\(_2\) ) and the forgotten index (F). In this article, we compute these indices of VC\(_5\)C\(_7[p;q]\) Nanotubes.

On the Second Order First Zagreb Index

Inspired by the chemical applications of higher-order connectivity index (or Randic index), we consider here the higher-order first Zagreb index of a molecular graph. In this paper, we study the linear regression analysis of the second order first Zagreb index with the entropy and acentric factor of an octane isomers. The linear model, based on the second order first Zagreb index, is better than models corresponding to the first Zagreb index and F-index. Further, we compute the second order first Zagreb index of line graphs of subdivision graphs of 2D-lattice, nanotube and nanotorus of TUC4C8[p; q], tadpole graphs, wheel graphs and ladder graphs.

Can we estimate the critical micelle concentration of amphiphilic drug bases from molecular connectivity indices?

Self-aggregation of drugs is since many years an important topic in the pharmaceutical sciences. Drugs can aggregate similar to surfactants and thereby exhibit a critical micelle concentration (CMC). The present work focused on amphiphilic drug bases and it was aimed to predict log(CMC) based on chemical structure alone. A dataset of 35 compounds was gathered mostly form the literature and complemented with own measurements based on ultrasonic resonator technology. The hydrophilic–lipophilic balance (HLB) values of the protonated bases were calculated and provided a range of 22.9–27.4. Based on a hypothesis from surfactant sciences, it was tried to predict log(CMC) with connectivity and shape indices as well as molecular dipole moment. A fairly good model was obtained using the Randix index (RI), 3 D Wiener number (WN) and molecular dipole moment (DM) (R2 = 0.824). Interestingly, a simple linear regression of log(CMC) with the Randic index alone, resulted in an acceptable model (R2 = 0.755). The present work should help with early identification of drug bases that exhibit surfactant-like behavior and an estimation of log(CMC) values is proposed. An improved understanding of drug aggregation and prediction of log(CMC) helps to better cope with physical consequences like, for example, “anomalous” drug solubility in drug discovery and development.

Computational Regression and Prediction Analysis on a Dataset of 52 Pyrrolo[2,3-b]Pyridines and Pyrimidines Rheumatoid Arthritis Inhibitors

Objectives: To evaluate the dependency of physico-chemical properties of a set of BTK inhibitors on activity by linear regression analysis. Methods/Statistical Analysis: A multivariate regression analysis was implemented on 52 Pyrrolo[2,3-b]pyridines and pyrimidines which are reported as Bruton's Tyrosine Kinase (BTK) inhibitors to construct a regression model using complete data set in the relationship between dependent variable and independent variable was estimated using python based regression analysis. Leverages were calculated in order to exclude outlying data from analysis Findings: A linear regression analysis on a complete dataset of BTK inhibitors as dependent variables and few independent variables resulted in F-test: 4.87, r value: 0.737 and r2 value of 0.543, respectively. The dataset investigated for the existence of outliers resulted in 50 BTK inhibitors after excluding 4q and 4zd from the dataset which resulted in improved r2 of 0.701 with better statistics. Further 44 compound training set resulted in improved r and r2 coefficients such as r: 0.816 and r2: 0.666, respectively and applying on a 6 compound validation set which determines regression model reliability and significance. Application/Improvements: Application of regression model to screen novel compounds with decreased H-bond acceptors, logP and KAlpha2 followed by an increase in KAlpha3 and randic index would enhance inhibitory activity against BTK. 1. Introduction Rheumatoid Arthritis (RA) is an autoimmune disease categorized by auto antibody circulation in plasma, inflammation in synovial, destruction of cartilage and bone etc.1,2 Bruton's Tyrosine Kinase (BTK) belongs to Tec kinase member family of enzymes which are necessary for activation of B-cells.3 A designated function for BTK is found in activation of cells mediated by BCR and cell survival.4-6 Compounds which inhibit BTK are known to hinder B cell receptor signaling7, several such inhibitors are currently in clinical trials and the first BTK inhibitor Ibrutinib was approved for treating mantle cell lymphoma. 8 Efforts from medicinal chemistry, synthesis, crystallography has led to the discovery of some non-covalent BTK inhibitory compounds. Several BTK inhibitors such as Pyrrolo[2,3-b]pyridines9, Pyrrolo[2,3-d]pyrimidines10, thieno[3,2-c]pyridin-4-amines11, phenylpyridin-2(1H)- ones12, Imidazo[1,5-a]quinoxalines13, Purine derivatives14, CarbazoleCarboxamides15, PyridazinoneAnalogs16, Diaminopyrimidines17, imidazo[1,5‑a]pyrazines18 are reported. In this paper, linear regression analysis was implemented to study the dependency of physico-chemical properties on

Inverse degree, Randic index and harmonic index of graphs

Let G be a graph with vertex set V and edge set E. Let di be the degree of the vertex vi of G. The inverse degree, Randic index, and harmonic index of G are defined as ID = ?vi?V 1/di, R = ? vivj?E 1/?di dj , and H = ? vivj?E 2=(di + dj), respectively. We obtain relations between ID and R as well as between ID and H. Moreover, we prove that in the case of trees, ID > R and ID > H.

Predicting Some Physicochemical Properties of Octane Isomers: A Topological Approach Using <i>ev</i>-Degree and <i>ve</i>-Degree Zagreb Indices

Topological indices have important role in theoretical chemistry for QSPR researches. Among the all topological indices the Randic and the Zagreb indices have been used more considerably than any other topological indices in chemical and mathematical literature. Most of the topological indices as in the Randic and the Zagreb indices are based on the degrees of the vertices of a connected graph. Recently novel two degree concepts have been defined in graph theory; ev-degrees and ve-degrees. In this study ev-degree Zagreb index, ve-degree Zagreb indices and ve-degree Randic index are defined by using these new graph invariants as parallel to their corresponding classical degree versions. These new group ev-degree and ve-degree indices are compared with the other well-known and most used topological indices in literature such as; Wiener, Zagreb and Randic indices by modelling some physicochemical properties of octane isomers. The ev-degree Zagreb index, the ve-degree Zagreb and the ve-degree Randic indices give better correlation than Wiener, Zagreb and Randic indices to predict the some specific physicochemical properties of octanes. The relations between the second Zagreb index and ev-degree and ve-degree Zagreb indices and some mathematical properties of ev-degree and ve-degree Zagreb indices are investigated.

Some Degree-Based Topological Indices of Base-3 Sierpiński Graphs

In this paper, a recursive relation between base-3 Sierpinski graphs rank n and n-1 of some topostructural indices is studied. Based on this relation, The formulae of the First Zagreb index, Second Zagreb index, Randic connectivity index, sum-connectivity index, Geometric-Arithmetic index and Atom-Bond Connectivity index of base-3 Sierpinski graphs are derived.

Computation of topological indices of mesh, grid, torus and cylinder

In this paper, we compute ABC index, Randic connectivity index, Sum connectivity index and GA index of grid, extended grid, torus and cylinder.