Disjoint Hamilton cycles in the star graph

On the construction of all shortest node-disjoint paths in star networks

“…. , t m ) in an n-star is greater than 80%, 88%, 80%, 77%, and 92% for (m, n) = (2, 3), (2,4), (3,5), (4,6), and (3, 7), respectively.…”

“…One crucial step in designing a multiprocessor system is to determine the topology of its interconnection network (network for short) in which nodes and links correspond to processors and communication channels, respectively. Among the network topologies proposed in the literature, the star network has received much attention from outstanding researchers [1,2,4,5,8,12,13,15]. …”

“…In order to figure out the probability that there exist disjoint shortest paths in a star network, bruteforce computations were carried out for verifying the sufficient condition on all the combinations of the source node and target nodes by running computer programs. In the situation that all of the source node and target nodes are mutually distinct, computational results have shown that the probability of the existence of the m disjoint shortest paths in the n-star is greater than 80%, 88%, 80%, 77%, and 92% for (m, n) = (2, 3), (2,4), (3,5), (4,6), and (3, 7), respectively.…”

Worst-case efficient dominating sets in digraphs

“…Thus, such a copy of ST 4 contains 12 oriented ±stable copies of ST 3 , namely those 12 6-cycle dags. Each of these copies may be used to define a map ζ as in (4) to prove that the chain D in (5) above is segmental.…”

“…Hamiltonian? Strongly Hamiltonian traceable as in [4,7], in a directed sense? Hamiltonian connected, as conjectured in [4,8] for the star graphs?…”