Ring Embedding in Faulty Star Graphs

概要

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In this paper, we consider the ring embedding problem in faulty star graphs. Our embedding is based on the path transition scheme and node borrow technique in the ring of 4-dimensional substars with evenly distributed faults. Let S_n be the n-dimensional star graph having n! nodes. We will show that a ring of length n! - 2f can be found in S_n when the number of faulty nodes f is at most n - 3. In the worst case, the loss of 2f nodes in the size of fault-free ring is inevitable because the star graph is bipartite. In addition, this result is superior to the best previous result [15] that constructs the ring of length n! - 4f under the same fault condition. Moreover, by extending this result into the star graph with both node and edge faults simultaneously, we can find the fault-free ring of length n! - 2f_n in S_n when it contains f_n faulty nodes and f_e faulty edges such that f_n + f_e <__- n - 3.
社団法人電子情報通信学会の論文
1999-09-25