The cordiality of the sum and union of two fourth power of paths and cycles
Elrokh, A., Rabie, A. (2021). The cordiality of the sum and union of two fourth power of paths and cycles. EKB Journal Management System, 29(1), 1-13. doi: 10.1186/s42787-020-00111-6
Ashraf Elrokh; Aya Rabie. "The cordiality of the sum and union of two fourth power of paths and cycles". EKB Journal Management System, 29, 1, 2021, 1-13. doi: 10.1186/s42787-020-00111-6
Elrokh, A., Rabie, A. (2021). 'The cordiality of the sum and union of two fourth power of paths and cycles', EKB Journal Management System, 29(1), pp. 1-13. doi: 10.1186/s42787-020-00111-6
Elrokh, A., Rabie, A. The cordiality of the sum and union of two fourth power of paths and cycles. EKB Journal Management System, 2021; 29(1): 1-13. doi: 10.1186/s42787-020-00111-6

The cordiality of the sum and union of two fourth power of paths and cycles

Journal of the Egyptian Mathematical Society
Volume 29, Issue 1, 2021, Page 1-13  XML PDF (3.09 MB)
Document Type: Original Article
DOI: 10.1186/s42787-020-00111-6
View on SCiNiTO View on SCiNiTO
Authors
Ashraf Elrokh1; Aya Rabie email 2
1Department of Mathematics, Faculty of Science, Menoufia University, Shebin El Kom, Egypt.
2Institute of National Planning, Cairo, Egypt.
Abstract
In the previous works, the limiting case for the motion of a rigid body about a fixed
point in a Newtonian force field, which comes from a gravity center lies on Z-axis, is
solved. The authors apply the small parameter technique which is achieved giving the
body a sufficiently large angular velocity component ro about the fixed z-axis of the
body. The periodic solutions of motion are obtained in neighborhood ro tends to ∞ . In
our work, we aim to find periodic solutions to the problem of motion in the neighborhood
of r0 tends to 0 . So, we give a new assumption that: ro is sufficiently small. Under
this assumption, we must achieve a large parameter and search for another technique
for solving this problem. This technique is named; a large parameter technique instead
of the small one well known previously. We see the advantage of the new technique
which appears in saving high energy used to begin the motion and give the solution of
the problem in another domain. The obtained solutions by the new technique depend
on ro. We consider that the center of mass of this body does not necessarily coincide
with the fixed point O. We reduce the six nonlinear differential equations of the body
and their three first integrals to a quasilinear autonomous system of two degrees of
freedom and one first integral. We solve the rational case when the frequencies of the
generating system are rational except ( = 1, 2, 1/2, 3, 1/3, . . .) under the condition
 ′′
0
= cos o ≈ 0 . We use the fourth-order Runge–Kutta method to find the periodic
solutions in the closed interval of the time t and to compare the analytical method
with the numerical one.
Keywords
Fourth power; Sum graph; Union graph; Cordial graph
Statistics
Article View: 60
PDF Download: 22