2 research outputs found
Fault-Tolerant Path-Embedding of Twisted Hypercube-Like Networks THLNs
The twisted hypercube-like networks() contain several important
hypercube variants. This paper is concerned with the fault-tolerant
path-embedding of -dimensional(-) . Let be an -
and be a subset of with . We show
that for arbitrary two different correct vertices and , there is a
faultless path of every length with , where if vertices and form a normal
vertex-pair and if vertices and form a weak vertex-pair in
()
Hamiltonian cycles in hypercubes with faulty edges
Szepietowski [A. Szepietowski, Hamiltonian cycles in hypercubes with
faulty edges, Information Sciences, 215 (2012) 75--82] observed that the
hypercube is not Hamiltonian if it contains a trap disconnected halfway.
A proper subgraph is disconnected halfway if at least half of its nodes
have parity 0 (or 1, resp.) and the edges joining all nodes of parity 0 (or 1,
resp.) in with nodes outside , are faulty. The simplest examples of such
traps are: (1) a vertex with incident faulty edges, or (2) a cycle
, where all edges going out of the cycle from and are
faulty. In this paper we describe all traps disconnected halfway with the
size , and discuss the problem whether there exist small sets of
faulty edges which preclude Hamiltonian cycles and are not based on sets
disconnected halfway. We describe heuristic which detects sets of faulty edges
which preclude HC also those sets that are not based on subgraphs disconnected
halfway. We describe all cubes that are not Hamiltonian, and all
cubes with 8 or 9 faulty edges that are not Hamiltonian