Analyzing the boron triangular nanotube through topological indices via <i>M</i>-polynomial

Hussain, Sabir; Afzal, Farkhanda; Afzal, Deeba; Cancan, Murat; Ediz, Süleyman; Farahani, Mohammad Reza

doi:10.1080/09720529.2021.1882158

Cited by 11 publications

(3 citation statements)

References 25 publications

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“…for x and y. The calculation of topological indices using M-polynomial in the molecular graphs has also been investigated [6,19]. Definition 5.…”

Section: Introductionmentioning

confidence: 99%

Investigating Banhatti indices on the molecular graph and the line graph of Glass with M-polynomial approach

Ghods,

Ramezani Tousi

2024

Proyecciones (Antofagasta)

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Topological indices are numerical values related to a chemical structure that describes the correlation of chemical structure with different physical properties and chemical reactions. Glass has wide applications in architecture, tableware, optics, and optoelectronics. In this article, first, the mathematical relationship between M-polynomial and Banhatti indices such as K-Banhatti, d-Banhatti, and hyper d-Banhatti indices are obtained. Then using M-polynomial, Banhatti indices are calculated.

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“…for x and y. The calculation of topological indices using M-polynomial in the molecular graphs has also been investigated [6,19]. Definition 5.…”

Section: Introductionmentioning

confidence: 99%

Investigating Banhatti indices on the molecular graph and the line graph of Glass with M-polynomial approach

Ghods,

Ramezani Tousi

2024

Proyecciones (Antofagasta)

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“…M-polynomial of a boron three-sided nanotube can recuperate the topological indices which are reliant upon the level of the vertex. We have introduced the outcomes in a graphical structure [23].…”

Section: Introductionmentioning

confidence: 99%

Optimized Evaluation of Mobile Base Station by Modern Topological Invariants

Hamid¹,

Iqbal²,

Ashraf³

et al. 2023

CMC

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Due to a tremendous increase in mobile traffic, mobile operators have started to restructure their networks to offload their traffic. New research directions will lead to fundamental changes in the design of future Fifthgeneration (5G) cellular networks. For the formal reason, the study solves the physical network of the mobile base station for the prediction of the best characteristics to develop an enhanced network with the help of graph theory. Any number that can be uniquely calculated by a graph is known as a graph invariant. During the last two decades, innumerable numerical graph invariants have been portrayed and used for correlation analysis. In any case, no efficient assessment has been embraced to choose, how much these invariants are connected with a network graph. This paper will talk about two unique variations of the hexagonal graph with great capability of forecasting in the field of optimized mobile base station topology in setting with physical networks. Since K-banhatti sombor invariants (KBSO) and Contrharmonic-quadratic invariants (CQIs) are newly introduced and have various expectation characteristics for various variations of hexagonal graphs or networks. As the hexagonal networks are used in mobile base stations in layered, forms called honeycomb. The review settled the topology of a hexagon of two distinct sorts with two invariants KBSO and CQIs and their reduced forms. The deduced outcomes can be utilized for the modeling of mobile cellular networks, multiprocessors interconnections, microchips, chemical compound synthesis and memory interconnection networks. The results find sharp upper bounds and lower bounds of the honeycomb network to utilize the Mobile base station network (MBSN) for the high load of traffic and minimal traffic also.

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“…In this work, various degree based descriptors of β 12 -Borophene nanosheet [2] are computed using M-polynomial approach. The structural descriptors of borophene nanosheets and borophene nanotubes of other variations, namely, 2−P mmn, χ 3 and honeycomb were studied by researchers [23,24,25]. In this paper, the β 12 -Borophene nanosheet is denoted as β 12 −BN (r, c), where r is the count of rows and c is the count of columns that hexagons with centre vertex are…”

Section: Introductionmentioning

confidence: 99%

A Novel Perspective for M-Polynomials to Compute Molecular Descriptors of Borophene Nanosheet

Xavier

Ismail

Ghani

et al. 2023

Preprint

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Nanomaterials feature exceptional, one-of-a-kind qualities that might be used in electronics, medicine, and other industries. Due to their unique photonic, electrical, catalytic, and magnetic capabilities as well as their use in helping immunotherapy, drug carriers, biosensors, electronic devices, etc., two dimensional materials are becoming considerably more important. Two-dimensional nanomaterials called borophene have a variety of intriguing characteristics. In the fields of chemistry, material science, nanotechnology, and condensed matter physics, they left an indelible impression thanks to their astounding physical and molecular characteristics. The concept of modelling the structure of a molecule or chemical network to a chemical graph and then quantitatively analysing the resulting graph with the aid of topological descriptors was a major advance in the fields of mathematics and chemistry. Topological descriptors are used in a wide range of fields, including chemistry, information technology, biology, quantitative structure-property relationships (QSPR), quantitative structure-activity relationships (QSAR), and many more. New descriptors that more closely connect with the structural characteristics of a chemical structure are being developed by researchers working on this idea. Finding a chemical graph's structural descriptors may be done in a variety of ways. It is discovered that the M-polynomial is a very versatile and quick method for computing the degree-based descriptors of chemical graphs or networks. The degree-based descriptors of the $\beta_{12}$-Borophene nanosheet are established in this study utilising the M-polynomial technique. At the conclusion, the numerical and graphical comparison based on the identified analytic expressions is also provided.

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Analyzing the boron triangular nanotube through topological indices via M-polynomial

Cited by 11 publications

References 25 publications

Investigating Banhatti indices on the molecular graph and the line graph of Glass with M-polynomial approach

Investigating Banhatti indices on the molecular graph and the line graph of Glass with M-polynomial approach

Optimized Evaluation of Mobile Base Station by Modern Topological Invariants

A Novel Perspective for M-Polynomials to Compute Molecular Descriptors of Borophene Nanosheet

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