Asset Details
Do you wish to reserve the book?
Strong Subgraph Connectivity of Digraphs
Hey, we have placed the reservation for you!
By the way, why not check out events that you can attend while you pick your title.
Oops! Something went wrong.
Looks like we were not able to place the reservation. Kindly try again later.
Are you sure you want to remove the book from the shelf?
Strong Subgraph Connectivity of Digraphs
Do you wish to request the book?
Strong Subgraph Connectivity of Digraphs
Please be aware that the book you have requested cannot be checked out. If you would like to checkout this book, you can reserve another copy
We have requested the book for you!
Your request is successful and it will be processed during the Library working hours. Please check the status of your request in My Requests.
Oops! Something went wrong.
Looks like we were not able to place your request. Kindly try again later.
Journal Article
Strong Subgraph Connectivity of Digraphs
2021
Overview
Let
D
=
(
V
,
A
)
be a digraph of order
n
,
S
a subset of
V
of size
k
and
2
≤
k
≤
n
. A strong subgraph
H
of
D
is called an
S
-
strong
subgraph if
S
⊆
V
(
H
)
. A pair of
S
-strong subgraphs
D
1
and
D
2
are said to be
arc-disjoint
if
A
(
D
1
)
∩
A
(
D
2
)
=
∅
. A pair of arc-disjoint
S
-strong subgraphs
D
1
and
D
2
are said to be
internally disjoint
if
V
(
D
1
)
∩
V
(
D
2
)
=
S
. Let
κ
S
(
D
)
(resp.
λ
S
(
D
)
) be the maximum number of internally disjoint (resp. arc-disjoint)
S
-strong subgraphs in
D
. The
strong subgraph
k
-connectivity
is defined as
κ
k
(
D
)
=
min
{
κ
S
(
D
)
∣
S
⊆
V
,
|
S
|
=
k
}
.
As a natural counterpart of the strong subgraph
k
-connectivity, we introduce the concept of
strong subgraph
k
-arc-connectivity
which is defined as
λ
k
(
D
)
=
min
{
λ
S
(
D
)
∣
S
⊆
V
(
D
)
,
|
S
|
=
k
}
.
A digraph
D
=
(
V
,
A
)
is called
minimally strong subgraph
(
k
,
ℓ
)
-(arc-)connected
if
κ
k
(
D
)
≥
ℓ
(resp.
λ
k
(
D
)
≥
ℓ
) but for any arc
e
∈
A
,
κ
k
(
D
-
e
)
≤
ℓ
-
1
(resp.
λ
k
(
D
-
e
)
≤
ℓ
-
1
). In this paper, we first give complexity results for
λ
k
(
D
)
, then obtain some sharp bounds for the parameters
κ
k
(
D
)
and
λ
k
(
D
)
. Finally, minimally strong subgraph
(
k
,
ℓ
)
-connected digraphs and minimally strong subgraph
(
k
,
ℓ
)
-arc-connected digraphs are studied.
Publisher
Springer Japan,Springer Nature B.V
