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research
Edge-Fault Tolerance of Hypercube-like Networks
Authors
Xiang-Jun Li
Jun-Ming Xu
Publication date
19 December 2012
Publisher
View
on
arXiv
Abstract
This paper considers a kind of generalized measure
Ξ»
s
(
h
)
\lambda_s^{(h)}
Ξ»
s
(
h
)
β
of fault tolerance in a hypercube-like graph
G
n
G_n
G
n
β
which contain several well-known interconnection networks such as hypercubes, varietal hypercubes, twisted cubes, crossed cubes and M\"obius cubes, and proves
Ξ»
s
(
h
)
(
G
n
)
=
2
h
(
n
β
h
)
\lambda_s^{(h)}(G_n)= 2^h(n-h)
Ξ»
s
(
h
)
β
(
G
n
β
)
=
2
h
(
n
β
h
)
for any
h
h
h
with
0
β©½
h
β©½
n
β
1
0\leqslant h\leqslant n-1
0
β©½
h
β©½
n
β
1
by the induction on
n
n
n
and a new technique. This result shows that at least
2
h
(
n
β
h
)
2^h(n-h)
2
h
(
n
β
h
)
edges of
G
n
G_n
G
n
β
have to be removed to get a disconnected graph that contains no vertices of degree less than
h
h
h
. Compared with previous results, this result enhances fault-tolerant ability of the above-mentioned networks theoretically
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Last time updated on 30/10/2017