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research
Constructing Two Edge-Disjoint Hamiltonian Cycles in Locally Twisted Cubes
Authors
Ruo-Wei Hung
Publication date
1 January 2010
Publisher
View
on
arXiv
Abstract
The
n
n
n
-dimensional hypercube network
Q
n
Q_n
Q
n
β
is one of the most popular interconnection networks since it has simple structure and is easy to implement. The
n
n
n
-dimensional locally twisted cube, denoted by
L
T
Q
n
LTQ_n
L
T
Q
n
β
, an important variation of the hypercube, has the same number of nodes and the same number of connections per node as
Q
n
Q_n
Q
n
β
. One advantage of
L
T
Q
n
LTQ_n
L
T
Q
n
β
is that the diameter is only about half of the diameter of
Q
n
Q_n
Q
n
β
. Recently, some interesting properties of
L
T
Q
n
LTQ_n
L
T
Q
n
β
were investigated. In this paper, we construct two edge-disjoint Hamiltonian cycles in the locally twisted cube
L
T
Q
n
LTQ_n
L
T
Q
n
β
, for any integer
n
β©Ύ
4
n\geqslant 4
n
β©Ύ
4
. The presence of two edge-disjoint Hamiltonian cycles provides an advantage when implementing algorithms that require a ring structure by allowing message traffic to be spread evenly across the locally twisted cube.Comment: 7 pages, 4 figure
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Last time updated on 30/10/2017