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Published in:
2005 | OriginalPaper | Chapter
Edge-Pancyclicity of Twisted Cubes
Authors : Jianxi Fan, Xiaola Lin, Xiaohua Jia, Rynson W. H. Lau
Published in: Algorithms and Computation
Publisher: Springer Berlin Heidelberg
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Twisted cubes are attractive alternatives to hypercubes. In this paper, we study a stronger pancyclicity of twisted cubes. We prove that the
n
-dimensional twisted cube is edge-pancyclic for
n
≥ 3. That is, for any (
x
,
y
) ∈
E
(
TQ
n
) (
n
≥ 3) and any integer
l
with 4 ≤
l
≤ 2
n
, a cycle
C
of length
l
can be embedded with dilation 1 into
TQ
n
such that (
x
,
y
) is in
C
. It is clear that an edge-pancyclic graph is also a node-pancyclic graph. Therefore,
TQ
n
is also a node-pancyclic graph for
n
≥ 3.