Yuan-Kang Shih and Shu-Li Chang and Shin-Shin Kao
The Spanning Laceability of kary ncubes when k is Even
1499 - 1507
2010
4
12
International Journal of Mathematical and Computational Sciences
https://publications.waset.org/pdf/14139
https://publications.waset.org/vol/48
World Academy of Science, Engineering and Technology
Qk
n has been shown as an alternative to the hypercube
family. For any even integer k ≥ 4 and any integer n ≥ 2, Qk
n is
a bipartite graph. In this paper, we will prove that given any pair of
vertices, w and b, from different partite sets of Qk
n, there exist 2n
internally disjoint paths between w and b, denoted by Pi 0 ≤ i ≤ 2n1, such that 2n1
i0 Pi covers all vertices of Qk
n. The result is
optimal since each vertex of Qk
n has exactly 2n neighbors.
Open Science Index 48, 2010