%0 Journal Article
	%A Chia-Jung Tsai and  Shin-Shin Kao
	%D 2009
	%J International Journal of Mathematical and Computational Sciences
	%B World Academy of Science, Engineering and Technology
	%I Open Science Index 35, 2009
	%T The Panpositionable Hamiltonicity of k-ary n-cubes
	%U https://publications.waset.org/pdf/2528
	%V 35
	%X The hypercube Qn is one of the most well-known
and popular interconnection networks and the k-ary n-cube Qk
n is
an enlarged family from Qn that keeps many pleasing properties
from hypercubes. In this article, we study the panpositionable
hamiltonicity of Qk
n for k ≥ 3 and n ≥ 2. Let x, y of V (Qk
n)
be two arbitrary vertices and C be a hamiltonian cycle of Qk
n.
We use dC(x, y) to denote the distance between x and y on the
hamiltonian cycle C. Define l as an integer satisfying d(x, y) ≤ l ≤ 1
2 |V (Qk
n)|. We prove the followings:
• When k = 3 and n ≥ 2, there exists a hamiltonian cycle C
of Qk
n such that dC(x, y) = l.
• When k ≥ 5 is odd and n ≥ 2, we request that l /∈ S
where S is a set of specific integers. Then there exists a
hamiltonian cycle C of Qk
n such that dC(x, y) = l.
• When k ≥ 4 is even and n ≥ 2, we request l-d(x, y) to be
even. Then there exists a hamiltonian cycle C of Qk
n such
that dC(x, y) = l.
The result is optimal since the restrictions on l is due to the
structure of Qk
n by definition.
	%P 889 - 895