Adjacent Vertices Fault Tolerance Hamiltonian Laceability of Star Graphs

• Main Authors: Chun-Yen Yang, 楊俊彥
• Other Authors: Chun-Nan Hung
• Format: Others
• Language: en_US
• Published: 2006
• Online Access: http://ndltd.ncl.edu.tw/handle/20553242106529293033

碩士 === 大葉大學 === 資訊工程學系碩士班 === 94 === Let Sn be an n-dimensional Star graph. In this paper, we show that Sn −F is Hamiltonian laceable where F is the set of f ≤(n−4) pairs of adjacent faulty vertices, Sn−F is Hamiltonian where F is the set of f ≤(n−3) pairs of adjacent faulty vertices. We also show that Sn −F is hyper-Hamiltonian laceable where F is the set of f ≤(n −4) pairs of adjacent faulty vertices. Applying these results, we also construct the fault-free cycle with length n! −2f + 2 in Sn −F’ where F’ is the faulty vertices set with at least a black vertex and a white vertex for |F’| = f ≤n−2 and the fault-free path with length n! −2f+ 1 for any two different color vertices in Sn−F’where F’is the faulty vertices set with at least a black vertex and a white vertex for |F`| = f ≤n−3 and n!−2f for any two same color vertices in Sn −F′where F′is the faulty vertices set for |F`| = f ≤n−3