Signed Product Cordial of the Sum and Union of Two Fourth Power of Paths and Cycles
Shokry Nada,
Amani Elrayes,
Ashraf Elrokh,
Aya Rabie
Issue:
Volume 4, Issue 4, December 2019
Pages:
45-50
Received:
15 June 2019
Accepted:
12 August 2019
Published:
30 December 2019
Abstract: A simple graph is said to be signed product cordial if it admits ±1 labeling that satisfies certain conditions. Our aim in this paper is to contribute some new results on signed product cordial labeling and present necessary and sufficient conditions for signed product cordial of the sum and union of two fourth power of paths. We also study the signed product cordiality of the sum and union of fourth power cycles The residue classes modulo 4 are accustomed to find suitable labelings for each class to achieve our task. We have shown that the union and the join of any two fourth power of paths are always signed product cordial. Howover, the join and union of fourth power of cycles are only signed codial with some expectional situations.
Abstract: A simple graph is said to be signed product cordial if it admits ±1 labeling that satisfies certain conditions. Our aim in this paper is to contribute some new results on signed product cordial labeling and present necessary and sufficient conditions for signed product cordial of the sum and union of two fourth power of paths. We also study the sig...
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Magneto-hydrodynamics (MHD) Bioconvection Nanofluid Slip Flow over a Stretching Sheet with Thermophoresis, Viscous Dissipation and Brownian Motion
Falana Ayodeji,
Alegbeleye Tope,
Olabanji Pele
Issue:
Volume 4, Issue 4, December 2019
Pages:
51-60
Received:
6 July 2019
Accepted:
18 August 2019
Published:
8 January 2020
Abstract: The bioconvection Magneto-Hydrodynamics (MHD) flow of nanofluid over a stretching sheet with velocity slip and viscous dissipation is studied. The governing nonlinear partial differential equations of the flow are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformation. These coupled ordinary differential equations are solved using fourth order Runge Kutta-Fehlberg integration method along with shooting technique. Solutions showing the effects of pertinent parameters on the velocity temperature, nanoparticles concentration, skin friction, Nusselt number and microorganism density are illustrated graphically and discussed. It is observed that there is enhancement of the motile microorganism density as thermal slip and Eckert number increase but microorganism density slip parameter have the opposite effect on the microorganism density. It is also found that an increase in Lewis number results in reduction of the volume fraction of nanoparticles and concentration boundary-layer thickness. Brownian motion, Nb and Eckert number, Ec decrease both local Nusselt number and local motile microorganism density but increases local Sherwood number. In addition, as the values of radiation parameter R increase, the thermal boundary layer thickness increases. Finally, thermophoresis parameter, Nt decreases both local Sherwood number, local Nuseselt number and local motile microorganism density. Comparisons of the present result with the previously published results show good agreement.
Abstract: The bioconvection Magneto-Hydrodynamics (MHD) flow of nanofluid over a stretching sheet with velocity slip and viscous dissipation is studied. The governing nonlinear partial differential equations of the flow are transformed into a system of coupled nonlinear ordinary differential equations using similarity transformation. These coupled ordinary d...
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