Affiliation:
1. School of Mathematics and Statistics, Qinghai Normal University , Xining , 810008 , PR China
2. Academy of Plateau Science and Sustainability, People’s Government of Qinghai Province and Beijing Normal University , Xining , 810008 , PR China
Abstract
Abstract
One of the symbolic parameters to measure the fault tolerance of a network is its connectivity. The
H
H
-structure connectivity and
H
H
-substructure connectivity extend the classical connectivity and are more practical. For a graph
G
G
and its connected subgraph
H
H
, the
H
H
-structure connectivity
κ
(
G
;
H
)
\kappa \left(G;\hspace{0.33em}H)
(resp.
H
H
-substructure connectivity
κ
s
(
G
;
H
)
{\kappa }^{s}\left(G;\hspace{0.33em}H)
) of
G
G
is the cardinality of a minimum subgraph set such that every element of the set is isomorphic to
H
H
(resp. every element of the set is isomorphic to a connected subgraph of
H
H
) in
G
G
, whose vertices removal disconnects
G
G
. In this article, we investigate the
H
H
-structure connectivity and
H
H
-substructure connectivity of the
n
n
-dimensional burnt pancake network
BP
n
{{\rm{BP}}}_{n}
for each
H
∈
{
K
1
,
K
1
,
1
,
…
,
K
1
,
n
−
1
,
P
4
,
…
,
P
7
,
C
8
}
H\in \left\{{K}_{1},{K}_{1,1},\ldots ,{K}_{1,n-1},{P}_{4},\ldots ,{P}_{7},{C}_{8}\right\}
.