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The star graph is viewed as an attractive alternative to the hypercube. In this paper, we investigate the Hamiltonicity of an n-dimensional star graph. We show that for any n-dimensional star graph (n?4) with at most 3n?10 faulty edges in which each node is incident with at least two fault-free edges, there exists a fault-free Hamiltonian cycle. Our result improves on the previously best known result for the case where the number of tolerable faulty edges is bounded by 2n?7. We also demonstrate that our result is optimal with respect to the worst case scenario, where every other node of a cycle of length 6 is incident with exactly n?3 faulty noncycle edges.

Prion diseases are fatal neurodegenerative disorders in human and animal associated with conformational conversion of a cellular prion protein (PrP C ) into the pathologic isoform (PrP Sc ). Various data indicate that the polymorphisms within the open reading frame (ORF) of PrP are associated with the susceptibility and control the species barrier in prion diseases. In the present study, partial Prnp from 25 Amur tigers (tPrnp) were cloned and screened for polymorphisms. Four single nucleotide polymorphisms (T423C, A501G, C511A, A610G) were found; the C511A and A610G nucleotide substitutions resulted in the amino acid changes Lysine171Glutamine and Alanine204Threoine, respectively. The tPrnp amino acid sequence is similar to house cat (Felis catus AF003087 ) and sheep, but differs significantly from other two cat Prnp sequences that were previousely deposited in GenBank.

The star graph has been recognized as an attractive alternative to the hypercube. In this paper, we investigate the hamiltoncity of a n-dimensional star graph. We show that for any n-dimensional star graph (n ges 4) with at most 3n - 10 faulty edges in which each node is incident to at least two fault-free edges, there exists a fault-free Hamiltonian cycle. Our result improves the previously best known result where the number of tolerable faulty edges is bounded by 2n - 7. We also demonstrate that our result is optimal with respect to the worst case scenario where every other node of a six-length cycle is incident to exactly n - 3 faulty non-cycle edges.

The prion protein gene of African lion (Panthera Leo) was first cloned and polymorphisms screened. The results suggest that the prion protein gene of eight African lions is highly homogenous. The amino acid sequences of the prion protein (PrP) of all samples tested were identical. Four single nucleotide polymorphisms (C42T, C81A, C420T, T600C) in the prion protein gene (Prnp) of African lion were found, but no amino acid substitutions. Sequence analysis showed that the higher homology is observed to felis catus AF003087 (96.7%) and to sheep number M31313.1 (96.2%) Genbank accessed. With respect to all the mammalian prion protein sequences compared, the African lion prion protein sequence has three amino acid substitutions. The homology might in turn affect the potential intermolecular interactions critical for cross species transmission of prion disease.