scholarly journals Computing the Hosoya Polynomial of M-th Level Wheel and Its Subdivision Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-7
Author(s):  
Peng Xu ◽  
Muhammad Numan ◽  
Aamra Nawaz ◽  
Saad Ihsan Butt ◽  
Adnan Aslam ◽  
...  
Keyword(s):  
Wiener Index ◽  
Topological Indices ◽  
Information Theoretic ◽  
Subdivision Graph ◽  
Hosoya Polynomial ◽  
Concept Of Information

The determination of Hosoya polynomial is the latest scheme, and it provides an excellent and superior role in finding the Weiner and hyper-Wiener index. The application of Weiner index ranges from the introduction of the concept of information theoretic analogues of topological indices to the use as major tool in crystal and polymer studies. In this paper, we will compute the Hosoya polynomial for multiwheel graph and uniform subdivision of multiwheel graph. Furthermore, we will derive two well-known topological indices for the abovementioned graphs, first Weiner index, and second hyper-Wiener index.

Efficiency, Sufficiency, and Optimality

2017 ◽  
Author(s):  
Amos Golan
Keyword(s):  
Limit Theorem ◽  
Computational Efficiency ◽  
The Other ◽  
Information Compression ◽  
Information Theoretic ◽  
Conditional Limit Theorem ◽  
Concept Of Information ◽  
Conditional Limit

In this chapter I provide additional rationalization for using the info-metrics framework. This time the justifications are in terms of the statistical, mathematical, and information-theoretic properties of the formalism. Specifically, in this chapter I discuss optimality, statistical and computational efficiency, sufficiency, the concentration theorem, the conditional limit theorem, and the concept of information compression. These properties, together with the other properties and measures developed in earlier chapters, provide logical, mathematical, and statistical justifications for employing the info-metrics framework.

Five results on maximizing topological indices in graphs

2021 ◽  
Vol vol. 23, no. 3 (Graph Theory) ◽  
Author(s):  
Stijn Cambie
Keyword(s):  
Independence Number ◽  
Wiener Index ◽  
Bipartite Graphs ◽  
Topological Indices ◽  
Matching Number ◽  
Extremal Graphs ◽  
Szeged Index ◽  
Complete Bipartite Graphs ◽  
The Difference

In this paper, we prove a collection of results on graphical indices. We determine the extremal graphs attaining the maximal generalized Wiener index (e.g. the hyper-Wiener index) among all graphs with given matching number or independence number. This generalizes some work of Dankelmann, as well as some work of Chung. We also show alternative proofs for two recents results on maximizing the Wiener index and external Wiener index by deriving it from earlier results. We end with proving two conjectures. We prove that the maximum for the difference of the Wiener index and the eccentricity is attained by the path if the order $n$ is at least $9$ and that the maximum weighted Szeged index of graphs of given order is attained by the balanced complete bipartite graphs.

scholarly journals On the Wiener index and variants of the Szeged index of single-walled titania nanotubes TiO2(m,n)

2017 ◽  
Vol 95 (1) ◽  
pp. 68-86 ◽  
Author(s):  
Muhammad Imran ◽  
Sabeel-e Hafi
Keyword(s):  
Physicochemical Properties ◽  
Strain Energy ◽  
Chemical Compounds ◽  
Wiener Index ◽  
Exact Expression ◽  
Topological Indices ◽  
Titania Nanotubes ◽  
Graph Invariant ◽  
Szeged Index ◽  
Cut Method

Topological indices are numerical parameters of a graph that characterize its topology and are usually graph invariant. There are certain types of topological indices such as degree-based topological indices, distance-based topological indices, and counting-related topological indices. These topological indices correlate certain physicochemical properties such as boiling point, stability, and strain energy of chemical compounds. In this paper, we compute an exact expression of Wiener index, vertex-Szeged index, edge-Szeged index, and total-Szeged index of single-walled titania nanotubes TiO2(m, n) by using the cut method for all values of m and n.

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.

Performance analysis of the “intelligent” Kirchhoff-Law-Johnson-Noise secure key exchange

2014 ◽  
Vol 33 ◽  
pp. 1460368
Author(s):  
Janusz Smulko
Keyword(s):  
Performance Analysis ◽  
Distribution System ◽  
Key Distribution ◽  
Key Exchange ◽  
Johnson Noise ◽  
Statistical Tools ◽  
Information Theoretic ◽  
The Wire ◽  
Averaging Time

The Kirchhoff-Law-Johnson-Noise (KLJN) secure key distribution system provides a way of exchanging information theoretic secure keys by measuring the random voltage and current through the wire connecting two different resistors at Alice's and Bob's ends. Recently new advanced protocols for the KLJN method have been proposed with enhanced performance. In this paper we analyze the KLJN system and compare with “intelligent” KLJN (iKLJN) scheme. This task requires the determination of the applied resistors and the identification of the various superpositions of known and unknown noise components. Some statistical tools to determine how the duration of the bit exchange window (averaging time) influences the performance of secure bit exchange will be explored.

Novel Applications of Topological Indices. 1. Prediction of the Ultrasonic Sound Velocity in Alkanes and Alcohols

1986 ◽  
Vol 41 (10) ◽  
pp. 1238-1244 ◽  
Author(s):  
D. H. Rouvray ◽  
W. Tatong
Keyword(s):  
Sound Velocity ◽  
Carbon Number ◽  
Wiener Index ◽  
Topological Indices ◽  
Regression Analyses ◽  
Velocity Data ◽  
Molecular Connectivity ◽  
Ultrasonic Sound ◽  
Connectivity Indices ◽  
Novel Applications

Several different topological indices (the carbon number, the Wiener index, the Balaban distance sum connectivity index, the Randić molecular identification number, and the Randić molecular connectivity indices 0χ, 1χ,,2χ, 3χp and 3χc ) were employed in the correlation of the velocity of ultrasonic sound in a variety of alkane and alcohol species. Using linear regression analyses and published sound velocity data, a number of excellent correlations were obtained for both alkanes and alcohols. Equations are developed which permit the prediction of sound velocity in these species to within 2% in most cases.

scholarly journals Topological indices of non-commuting graph of dihedral groups

2018 ◽  
Vol 14 ◽  
pp. 473-476 ◽  
Author(s):  
Nur Idayu Alimon ◽  
Nor Haniza Sarmin ◽  
Ahmad Erfanian
Keyword(s):  
Wiener Index ◽  
Topological Indices ◽  
First Zagreb Index ◽  
Dihedral Groups ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Commuting Graph ◽  
Vertex Set ◽  
Group A ◽  
Group Of Symmetries

Assume  is a non-abelian group  A dihedral group is the group of symmetries of a regular polygon, which includes rotations and reflections. The non-commuting graph of  denoted by  is the graph of vertex set  whose vertices are non-central elements, in which  is the center of  and two distinct vertices  and  are joined by an edge if and only if  In this paper, some topological indices of the non-commuting graph,  of the dihedral groups,  are presented. In order to determine the Edge-Wiener index, First Zagreb index and Second Zagreb index of the non-commuting graph,  of the dihedral groups,  previous results of some of the topological indices of non-commuting graph of finite group are used. Then, the non-commuting graphs of dihedral groups of different orders are found. Finally, the generalisation of Edge-Wiener index, First Zagreb index and Second Zagreb index of the non-commuting graphs of dihedral groups are determined.

scholarly journals QSPR model for the forecast of dynamic viscosity of arenas by the topological characteristics of molecules

2020 ◽  
Vol 62 (6) ◽  
pp. 1-6
Author(s):  
Mikhail Yu. Dolomatov ◽  
◽  
Timur M. Aubekerov ◽  
Oleg S. Koledin ◽  
Ella A. Kovaleva ◽  
...  
Keyword(s):  
Dynamic Viscosity ◽  
Wiener Index ◽  
Test Sample ◽  
Coefficient Of Determination ◽  
Saturated Hydrocarbons ◽  
Qspr Model ◽  
Proposed Model ◽  
Chemical Factors ◽  
Topological Characteristics

Prediction of the dynamic viscosity of saturated hydrocarbons vapors is an important step in the calculation of various processes and apparatuses in chemical technology. In order to quickly determine the dynamic viscosity without resorting to the use of expensive equipment, methods of mathematical modeling are currently used. To predict the dynamic viscosity of saturated arenas vapors, a nonlinear multivariate regression model QSPR is proposed. The model associates with a dynamic viscosity a set of descriptors – the topological characteristics of molecular graphs: the Randic index, the Wiener index, and also the functions of the eigenvalues of the topological matrix of the molecule, which reflect the main structural and chemical factors, such as branching, length of the carbon skeleton and energy parameters of molecules, for example, Hückel’s perturbation spectrum of molecules, as well as affecting dynamic viscosity. The objects of research used arenas. The studied sample included 40 hydrocarbons of a number of arenas. The proposed model adequately describes the dynamic viscosity of saturated arenas vapors. The coefficient of determination of the model is 0.986. The average absolute and relative error for the test sample of HF is -2.46⋅10-7 cP and 1.83%, respectively. The model is applicable for engineering and scientific forecasts of the dynamic viscosity of various saturated arenas vapors.

scholarly journals Hosoya polynomial of zigzag polyhex nanotorus

2008 ◽  
Vol 73 (3) ◽  
pp. 311-319 ◽  
Author(s):  
Mehdi Eliasi ◽  
Bijan Taeri
Keyword(s):  
Molecular Graph ◽  
Wiener Index ◽  
New Method ◽  
Second Derivative ◽  
First Derivative ◽  
Hosoya Polynomial

The Hosoya polynomial of a molecular graph G is defined as H(G,?)=?{u,v}V?(G) ?d(u,v), where d(u,v) is the distance between vertices u and v. The first derivative of H(G,?) at ?=1 is equal to the Wiener index of G, defined as W(G)?{u,v}?V(G)d(u,v). The second derivative of 1/2 ?H(G, ?) at ?=1 is equal to the hyper-Wiener index, defined as WW(G)+1/2?{u,v}?V(G)d(u,v)?. Xu et al.1 computed the Hosoya polynomial of zigzag open-ended nanotubes. Also Xu and Zhang2 computed the Hosoya polynomial of armchair open-ended nanotubes. In this paper, a new method was implemented to find the Hosoya polynomial of G = HC6[p,q], the zigzag polyhex nanotori and to calculate the Wiener and hyper Wiener indices of G using H(G,?).

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