Two Tight Independent Set Conditions for Fractional (g, f, m)-Deleted Graphs Systems

Gao, Wei; Guirao, Juan Luis García; Wu, H.

doi:10.1007/s12346-016-0222-z

Cited by 47 publications

(20 citation statements)

References 14 publications

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“…Thus, we study the data transmission problem by considering the Hamiltonian fractional (g, f )-factor and ID-Hamiltonian fractional (g, f )-factor in the networks model. Several related results can refer to [9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Topics on data transmission problem in software definition network

Gao¹,

Li²,

Xu³

et al. 2017

Open Physics

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Abstract:In normal computer networks, the data transmission between two sites go through the shortest path between two corresponding vertices. However, in the setting of software definition network (SDN), it should monitor the network traffic flow in each site and channel timely, and the data transmission path between two sites in SDN should consider the congestion in current networks. Hence, the difference of available data transmission theory between normal computer network and software definition network is that we should consider the prohibit graph structures in SDN, and these forbidden subgraphs represent the sites and channels in which data can't be passed by the serious congestion. Inspired by theoretical analysis of an available data transmission in SDN, we consider some computational problems from the perspective of the graph theory. Several results determined in the paper imply the sufficient conditions of data transmission in SDN in the various graph settings.

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Section: Introductionmentioning

confidence: 99%

Topics on data transmission problem in software definition network

Gao¹,

Li²,

Xu³

et al. 2017

Open Physics

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“…Then, the applied boundary conditions are dened according to the physics of the problem. [42][43][44][45][46][47][48][49][50][51] Since most of the engineering-related problems contain nonlinear terms in the main governing equations, various techniques have been developed to solve these equations.…”

Section: Problem Definitionmentioning

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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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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“…The concept of fractional (g, f , n , m)critical deleted graph can be regarded as a combination of fractional (g, f , n )-critical graph and fractional (g, f , m)-deleted graph, i.e., a graph G is fractional (g, f , n , m)-critical deleted if after n vertices are deleted from G, the rest of the graph is a fractional (g, f , m)-deleted graph. For some recent advances on the existence of a fractional factor in various settings, we can refer to Gao et al [7][8][9][10]12], Liu et al [18], and Zhou et al [34,35,37,[39][40][41][42][43].…”

Section: Background and Conceptsmentioning

confidence: 99%

Parameters and fractional factors in different settings

Gao

Guirao

2019

J Inequal Appl

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In computer networks, the feasibility of data transmission can be measured in terms of fractional factor model, and specifically the framework of fractional critical deleted graph can express the setting when certain sites and channels are unavailable at a special time. We study the relationship between some parameters in graphs and the existence of fractional (g, f )-factor in various settings here. Our main contributions are three-fold: first, a connectivity condition for a graph to be fractional (g, f , n , m)-critical deleted is determined; second, the relationship between independence number and fractional ID-(g, f , m)-deleted graphs is studied; third, an isolated toughness bound for fractional (g, f )-factors is given in balanced bipartite graph setting. Furthermore, by showing counterexamples we explain that bounds for parameters are tight in some sense, and corresponding conditions in all fractional factor settings are discussed as well. Finally, two open problems are proposed for future research. MSC: 05C70

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Two Tight Independent Set Conditions for Fractional (g, f, m)-Deleted Graphs Systems

Cited by 47 publications

References 14 publications

Topics on data transmission problem in software definition network

Topics on data transmission problem in software definition network

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

Parameters and fractional factors in different settings

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