Three algorithms for graph locally harmonious colouring

The impact of an axial magnetic field on the heat transfer and nanofluid flow among two horizontal coaxial tubes in the presence of thermal radiation was considered in this study. The impact of viscous dissipation was also considered. The well-known KKL (Koo-Kleinsteuer-Li) model was applied to approximate the viscosity of the nanofluid and the effective thermal conductivity. Furthermore, proper transformations for the velocity and temperature were applied in this study to obtain a set of ODEs (ordinary differential equations) for basic equations governing the flow, heat and mass transfer. In addition, the 4th order Runge-Kutta (RK) numerical scheme was applied to solve the differential equations along with the associated boundary conditions. The impacts of different parameters, including Hartmann number, Reynolds number, radiation parameter and aspect ratio, on the heat transfer and flow features were studied. According to the results, the value of the Nusselt number increases with an increase in the radiation parameter, Hartmann number and aspect ratio and a decrease in the Reynolds number and Eckert number. Fig. 8 Effect of aspect ratio on the Nusselt number and skin friction coefficient when Pr ¼ 6.8, h ¼ 0.5, Ec ¼ 0.01, Rd ¼ 0.1, Re ¼ 1, f ¼ 0.04.

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“…Optimized models can be used for better accuracy. [131][132][133][134][135][136][137][138][139][140][141][142][143][144][145][146][147][148][149]…”

Section: Methodsmentioning

confidence: 99%

A numerical simulation for magnetohydrodynamic nanofluid flow and heat transfer in rotating horizontal annulus with thermal radiation

et al. 2019

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“…Recently, the applications of Neural Network have been significantly increased in various engineering and industrial applications . Scholars and researchers have widely applied this method for the estimation of the results.…”

Section: Application Of Gmdh‐type Nn For Modeling Of the Problemmentioning

confidence: 99%

“…In this subject, theoretical methods have a significant deficiency for the evaluation of the main pattern of the results. So, several trainings required to be done to evaluate magnetohydrodynamic nanofluid convective heat transmission characteristics of materials and classifying experiential associations with an overall formula . Scientists and scholars have extensively tried to find a robust and reliable formula for the prediction of the heat transfer in popular domain.…”

Section: Introductionmentioning

confidence: 99%

Application of neural network on heat transfer enhancement of magnetohydrodynamic nanofluid

Gerdroodbary

2019

Heat Trans. Asian Res.

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“…The generalized honeycomb network [16] can be built from an infinite hexagonal system with no cut vertices or non-hexagonal interior faces. It is denoted by GH(n, p, q, r, s), and the structure can be developed using hexagons in various ways by fixing the parameters as n ≥ 1, 0 ≤ p ≤ r ≤ n, 0 ≤ s ≤ q ≤ n, and p + q = r + s, as shown in Figure 5.…”

Section: Generalized Honeycomb Networkmentioning

confidence: 99%

“…Clearly, the original harmonious coloring problem is the x/2 -harmonious coloring problem if x is the diameter of G. In addition, it was proven that solving the 1-harmonious coloring problem is NP-complete, and tight bounds were obtained for the path and cycle graphs, whereas the tight bounds for other graphs have been stated as open problems. Recently, Gao [15] presented three algorithms to give the coloring procedure for the 1-harmonious coloring problem, but these algorithms were based on an exhaustive search of vertices and branching rules.…”

Section: Introductionmentioning

confidence: 99%

Tight Bounds on 1-Harmonious Coloring of Certain Graphs

Liu

Arockiaraj²,

Nelson³

2019

Symmetry

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Graph coloring is one of the most studied problems in graph theory due to its important applications in task scheduling and pattern recognition. The main aim of the problem is to assign colors to the elements of a graph such as vertices and/or edges subject to certain constraints. The 1-harmonious coloring is a kind of vertex coloring such that the color pairs of end vertices of every edge are different only for adjacent edges and the optimal constraint that the least number of colors is to be used. In this paper, we investigate the graphs in which we attain the sharp bound on 1-harmonious coloring. Our investigation consists of a collection of basic graphs like a complete graph, wheel, star, tree, fan, and interconnection networks such as a mesh-derived network, generalized honeycomb network, complete multipartite graph, butterfly, and Benes networks. We also give a systematic and elegant way of coloring for these structures.

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Three algorithms for graph locally harmonious colouring

Cited by 24 publications

References 29 publications

A numerical simulation for magnetohydrodynamic nanofluid flow and heat transfer in rotating horizontal annulus with thermal radiation

A numerical simulation for magnetohydrodynamic nanofluid flow and heat transfer in rotating horizontal annulus with thermal radiation

Application of neural network on heat transfer enhancement of magnetohydrodynamic nanofluid

Tight Bounds on 1-Harmonious Coloring of Certain Graphs

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