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Embedding longest fault‐free paths in arrangement graphs with faulty vertices
Author(s) -
Lo RayShang,
Chen GenHuey
Publication year - 2001
Publication title -
networks
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.977
H-Index - 64
eISSN - 1097-0037
pISSN - 0028-3045
DOI - 10.1002/1097-0037(200103)37:2<84::aid-net3>3.0.co;2-a
Subject(s) - combinatorics , path graph , hypercube graph , embedding , distance , mathematics , graph , computer science , discrete mathematics , shortest path problem , graph power , line graph , artificial intelligence
The arrangement graph is a generalization of the star graph. Recent work by Hsieh et al. showed that an arrangement graph with faulty vertices contains a longest fault‐free cycle. In this paper, we generalize Hsieh et al.'s result by constructing a longest fault‐free path between two arbitrary distinct healthy vertices. Moreover, our result can tolerate more faulty vertices than can Hsieh et al.'s result. The situation of simultaneous faulty vertices and faulty edges is also discussed. © 2001 John Wiley & Sons, Inc.