TY - JFULL
AU - Yuan-Kang Shih and Shu-Li Chang and Shin-Shin Kao
PY - 2010/1/
TI - The Spanning Laceability of k-ary n-cubes when k is Even
T2 - International Journal of Mathematical and Computational Sciences
SP - 1498
EP - 1507
VL - 4
SN - 1307-6892
UR - https://publications.waset.org/pdf/14139
PU - World Academy of Science, Engineering and Technology
NX - Open Science Index 48, 2010
N2 - 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 ≤ 2n-1}, such that 2n-1
i=0 Pi covers all vertices of Qk
n. The result is
optimal since each vertex of Qk
n has exactly 2n neighbors.
ER -