Journal of KIISE:Computer Systems and Theory (한국정보과학회논문지:시스템및이론)

Korean Institute of Information Scientists and Engineers (한국정보과학회)
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Cycle Embedding of Faulty Recursive Circulants

고장난 재귀원형군의 사이클 임베딩

  • 박정흠 (가톨릭대학교 컴퓨터정보공학부)
  • Published : 2004.02.01
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Abstract

In this paper, we show that $ G(2^m, 4), m{\geq}3$with at most m-2 faulty elements has a fault-free cycle of length 1 for every ${\leq}1{\leq}2^m-f_v$ is the number of faulty vertices. To achieve our purpose, we define a graph G to be k-fault hypohamiltonian-connected if for any set F of faulty elements, G- F has a fault-free path joining every pair of fault-free vertices whose length is shorter than a hamiltonian path by one, and then show that$ G(2^m, 4), m{\geq}3$ is m-3-fault hypohamiltonian-connected.

이 논문에서는 재귀원형군 $ G(2^m, 4), m{\geq}3$은 고장인 요소의 수가 m-2개 이하일 때, 임의의 1, 4 ${\leq}1{\leq}2^m-f_v$에 대하여 길이 1인 고장 없는 사이클을 가짐을 보인다. 여기서, f$_{v}$ 는 고장 정점의 수이다. 이를 위하여, ｜F｜$\leq$k인 임의의 고장 요소 집합 F에 대해서 G-F가 임의의 두 정점을 잇는 길이가 해밀톤 경로보다 하나 작은 경로를 가질 때, G를 k-고장 하이포해밀톤 연결된 그래프라고 정의하고, $ G(2^m, 4), m{\geq}3$은 m-3-고장 하이포해밀톤 연결된 그래프임을 보인다.

Keywords

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