Fault-Tolerant Ring Embedding in Faulty Arrangement Graphs
نویسندگان
چکیده
The arrangement graph A n , k , which is a generalization of the star graph (n k = l), presents more flexibility than the star graph in adjusting the major design parameters: number o f nodes, degree , and diameter. Previously the arrangement graph has proven hamiltonian. In this p a p e r 'we further show that the arrangement graph remains hamiltonian even if it is faulty. Let IFe/ and IF,[ denote the numbers of edge faults and vertex faults, respectively. We show that A n , k is hamiltonian when (1) (k = 2 and n k >_ 4, o r k 2 3 and n k 2 4+ r;]), and IF,I 5 k ( n k ) 2 , or (2) k 2 2 , n k 2 2+[$1, and IF,/ 5 k ( n k 3 ) 1 , or (3) k 2 2 , n k 2 3, and IF,] 5 k .
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