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Journal Article
On structure and substructure fault tolerance of star networks
2023
Overview
Let
H
and
M
be two connected subgraphs of an interconnection network
G
. If the removal of any minimum
H
-structure-cut (resp.
H
-substructure-cut) isolates a component isomorphic to
M
, then
G
is said to be
super
H
|
M
-connected
(resp.
super sub
-
H
|
M
-
connected
). Furthermore, if the removal of any minimum
H
-structure-cut (resp. minimum
H
-substructure-cut) splits
G
into exactly two components, one of which is isomorphic to
M
, then
G
is said to be
hyper
H
|
M
-connected
(resp.
hyper sub
-
H
|
M
-
connected
). The
n
-dimensional star network
S
n
is one of alternative interconnection networks for multiprocessor systems. Let
n
≥
4
. In this paper, we prove that
S
n
is hyper
H
|
K
1
-connected and hyper sub-
H
|
K
1
-connected for
H
∈
{
K
1
,
r
,
P
5
}
and
1
≤
r
≤
n
-
3
,
S
n
is hyper
P
4
|
K
1
,
1
-connected and hyper sub-
P
4
|
K
1
,
1
-connected,
S
n
with
n
≥
5
is super
C
6
|
K
1
-connected, and
S
n
is hyper sub-
C
6
|
K
1
-connected, where
K
1
is the complete graph on one vertex and
K
1
,
r
is a star on
1
+
r
vertices,
P
k
is a path on
k
vertices and
C
6
is a cycle on 6 vertices.
Publisher
Springer US,Springer Nature B.V
Subject
