On computation of<i>M</i>-polynomial and topological indices of starphene graph

Chaudhry, Faryal; Ehsan, Muhammad; Afzal, Deeba; Farahani, Mohammad Reza; Cancan, Murat; Ediz, Süleyman

doi:10.1080/09720529.2021.1888434

Cited by 4 publications

(4 citation statements)

References 24 publications

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“…Many studies have done about the M-Polynomial such as computation of M-polynomial book graph and starphene graph in [9,10]. Also Basavanagoud, and et al obtained the M-polynomial of some graph operations and cycle related graphs in [11].…”

Section: Figure 1: G(o)hmentioning

confidence: 99%

“…Unlike the other graph polynomials through this polynomial, we can easily compute more than one degree based topological indices such as Atom bond connectivity index, Geometric connectivity index and some other indices by a certain derivative or integral or sometimes both. Some formula for computing those indices from the M-Polynomial are found in [8][9][10][11][12][13][14] as we illustrate some of these formulas in the following [8] where used operators are defined as [8][9][10][12][13][14]: One of the most recent defined degree based topological indices is Nirmala index defined by Kulli in 2021 [15], which is defined as follows:…”

Section: Figure 1: G(o)hmentioning

confidence: 99%

“…For a graph 𝐺, the M-Polynomial is defined by:𝑀(𝐺, 𝑥, 𝑦) = ∑ 𝑖≤𝑗 𝑚 𝑖𝑗 (𝐺)𝑥 𝑖 𝑦 𝑗 ••••••••••••••••• (1)where 𝑖, 𝑗 ≥ 1 and 𝑚 𝑖𝑗 is the number of (i,j)-edges of G, such that 𝑖 = 𝑑 𝐺 (𝑢), and 𝑗 = 𝑑 𝐺 (𝑣) for some vertices u,v ∈G. We can see that the M-Polynomial for a graph 𝐺 also can be represent as: 𝑀(𝐺, 𝑥, 𝑦) = ∑ 𝑒=𝑢𝑣∈𝐸(𝐺) 𝑥 𝑑 𝐺 (𝑢) 𝑦 𝑑 𝐺 (𝑣) ••••••••••••••• (2)Many studies have done about the M-Polynomial such as computation of M-polynomial book graph and starphene graph in[9,10]. Also Basavanagoud, and et al obtained the M-polynomial of some graph operations and cycle related graphs in[11].…”

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The M-Polynomial and Nirmala index of Certain Composite Graphs

Karim¹,

Arif²,

Ramadan³

2022

Tikrit J. Pure Sci.

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The M-Polynomial and Nirmala index are considered as two of the most recent found and important subjects in chemical graph theory. In this paper we drive and prove the computing formula of Nirmala index from the M-Polynomial, then compute the M-Polynomial for some certain composite graphs, and the Nirmala index via the computed M-Polynomial. The composite graphs are new defined graphs Kn(Pt)Km , Cn(e)Kn , and others obtained from simple graphs by certain graph operations such as join, corona, and cluster of any graph with some special graphs such as complete, path, …etc

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Section: Figure 1: G(o)hmentioning

confidence: 99%

Section: Figure 1: G(o)hmentioning

confidence: 99%

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confidence: 99%

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The M-Polynomial and Nirmala index of Certain Composite Graphs

Karim¹,

Arif²,

Ramadan³

2022

Tikrit J. Pure Sci.

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“…A chemical graph is the result of the molecular design by applying some graph The exhibit of chemical mixtures with the M-polynomials is a creating thought and the M-polynomial of various molecular structures upholds us to ascertain numerous topological indices. In this paper we ascertain M-polynomial and topological indices for the starphene graph, then, at that point, we recuperate various topological indices utilizing the M-polynomials [22].…”

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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