The bipanconnectivity and m -panconnectivity of the folded hypercube
The interconnection network considered in this paper is the folded hypercube that is an attractive variance of the well-known hypercube. The folded hypercube is superior to the hypercube in many criteria, such as diameter, connectivity and fault diameter. In this paper, we study the path embedding a...
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Published in | Theoretical computer science Vol. 385; no. 1; pp. 286 - 300 |
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Main Author | |
Format | Journal Article |
Language | English |
Published |
Amsterdam
Elsevier B.V
15.10.2007
Elsevier |
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Abstract | The interconnection network considered in this paper is the folded hypercube that is an attractive variance of the well-known hypercube. The folded hypercube is superior to the hypercube in many criteria, such as diameter, connectivity and fault diameter. In this paper, we study the path embedding aspects, bipanconnectivity and
m
-panconnectivity, of the
n
-dimensional folded hypercube. A bipartite graph is bipanconnected if each pair of vertices
x
and
y
are joined by the bipanconnected paths that include a path of each length
s
satisfying
N
−
1
≥
s
≥
dist
(
x
,
y
)
and
s
-
dist
(
x
,
y
)
is even, where
N
is the number of vertices, and
dist
(
x
,
y
)
denotes the shortest distance between
x
and
y
. A graph is
m
-panconnected if each pair of vertices
x
and
y
are joined by the paths that include a path of each length ranging from
m
to
N
−
1
. In this paper, we introduce a new graph called the Path-of-Ladders. By presenting algorithms to embed the Path-of-Ladders into the folded hypercube, we show that the
n
-dimensional folded hypercube is bipanconnected for
n
is an odd number. We also show that the
n
-dimensional folded hypercube is strictly
(
n
−
1
)
-panconnected for
n
is an even number. That is, each pair of vertices are joined by the paths that include a path of each length ranging from
n
−
1
to
N
−
1
; and the value
n
−
1
reaches the lower bound of the problem. |
---|---|
AbstractList | The interconnection network considered in this paper is the folded hypercube that is an attractive variance of the well-known hypercube. The folded hypercube is superior to the hypercube in many criteria, such as diameter, connectivity and fault diameter. In this paper, we study the path embedding aspects, bipanconnectivity and
m
-panconnectivity, of the
n
-dimensional folded hypercube. A bipartite graph is bipanconnected if each pair of vertices
x
and
y
are joined by the bipanconnected paths that include a path of each length
s
satisfying
N
−
1
≥
s
≥
dist
(
x
,
y
)
and
s
-
dist
(
x
,
y
)
is even, where
N
is the number of vertices, and
dist
(
x
,
y
)
denotes the shortest distance between
x
and
y
. A graph is
m
-panconnected if each pair of vertices
x
and
y
are joined by the paths that include a path of each length ranging from
m
to
N
−
1
. In this paper, we introduce a new graph called the Path-of-Ladders. By presenting algorithms to embed the Path-of-Ladders into the folded hypercube, we show that the
n
-dimensional folded hypercube is bipanconnected for
n
is an odd number. We also show that the
n
-dimensional folded hypercube is strictly
(
n
−
1
)
-panconnected for
n
is an even number. That is, each pair of vertices are joined by the paths that include a path of each length ranging from
n
−
1
to
N
−
1
; and the value
n
−
1
reaches the lower bound of the problem. |
Author | Fang, Jywe-Fei |
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Cites_doi | 10.1016/0095-8956(76)90061-7 10.1109/12.2234 10.1145/2465.2467 10.1002/net.20039 10.1109/12.628393 10.1080/00207160008804962 10.1016/S0020-0190(03)00258-8 10.1006/jpdc.2000.1681 10.1109/12.250606 10.1109/71.80187 10.1093/comjnl/46.6.632 10.1016/j.jpdc.2005.06.014 10.1016/j.ipl.2004.09.026 10.1016/j.disc.2005.12.011 10.1109/71.89068 10.1109/12.376173 10.1016/S0012-365X(97)80334-2 10.1016/j.disc.2004.08.005 10.1109/2.74 10.1016/S0020-0190(01)00226-5 10.1016/j.aml.2005.04.002 10.1016/0012-365X(91)90417-Z 10.1109/71.224219 10.1002/net.20002 10.1016/j.ipl.2004.03.009 10.1145/360336.360343 |
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Keywords | Folded hypercubes Algorithms Interconnection networks Panconnectivity Interconnection network Lower bound Graph path Computer theory Embedding Algorithm Variance Graph connectivity Interconnection Hypercube Bipartite graph Distance |
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Snippet | The interconnection network considered in this paper is the folded hypercube that is an attractive variance of the well-known hypercube. The folded hypercube... |
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SubjectTerms | Algorithmics. Computability. Computer arithmetics Algorithms Applied sciences Computer science; control theory; systems Exact sciences and technology Folded hypercubes Information retrieval. Graph Interconnection networks Miscellaneous Panconnectivity Theoretical computing |
Title | The bipanconnectivity and m -panconnectivity of the folded hypercube |
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