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

한국정보과학회 (Korean Institute of Information Scientists and Engineers)
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두 개의 랩어라운드 에지를 갖는 메쉬의 고장 해밀톤 성질

Fault Hamiltonicity of Meshes with Two Wraparound Edges

  • 발행 : 2003.08.01
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⟨ 이전 논문 다음 논문 ⟩

초록

본 논문에서는 첫 행과 마지막 행에 두개의 랩어라운드 에지를 갖는 m$\times$n (m$\geq$2, n$\geq$3) 메쉬 연결망에서의 고장 해밀톤 성질들에 대해 고려한다. 제시한 연결망이 n이 홀수일 때 해밀톤 연결된 그래프이며 1-고장 해밀톤 사이클을 지님을 보인다. 그리고 n이 짝수일 때 강한 해밀톤 laceable 그래프이며 1-정점 고장 강한 해밀톤 laceable 그래프임을 보인다.

In this paper, we consider the hamiltonian properties of m$\times$n (m$\geq$2, n$\geq$3) mesh networks with two wraparound edges on the first row and last row, called M$_2$(m, n), in the presence of a faulty node or link. We prove that M$_2$(m, n) with odd n is hamiltonian-connected and 1-fault hamiltonian. In addition, we prove that M$_2$(m, n) with even n is strongly hamiltonian laceable and 1-vertex fault tolerant strongly hamiltonian laceable.

키워드

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