Fault-Tolerant Hamiltonian Connectivity of Twisted Hypercube-Like Networks THLNs

The twisted hypercube-like networks (THLNs) include some well-known hypercube variants. A graph
$G$
is
$k$
-fault-tolerant Hamiltonian connected if
$G-F$
remains Hamiltonian connected for every
$F\subset V(G)\cup E(G)$
with
$|F|\leq k$
. This paper is concerned with the fault-tolerant Hamiltonian connectivity of an
$n$
-dimensional (
$n$
-D) THLN. Let
$G_{n}$
be an
$n$
-D THLN (
$n\geq 5$
) and
$F$
be a subset of
$V(G_{n})\cup E(G_{n})$
with
$|F|\leq n-2$
. We show that for arbitrary vertex-pair
$(u,v)$
in
$G_{n}-F$
, there exists a
$(n-2)$
-fault-tolerant Hamiltonian path joining vertices
$u$
and
$v$
except
$(u,v)$
being a weak vertex-pair in
$G_{n}-F$
. The technical theorem proposed in this paper can be applied to several multiprocessor systems, including
$n$
-D crossed cubes
$CQ_{n}$
,
$n$
-D twisted cubes
$TQ_{n}$
for odd
$n$
,
$n$
-D locally twisted cubes
$LTQ_{n}$
, and
$n$
-D Möbius cubes
$MQ_{n}$
.