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Conditional Edge-Fault Hamiltonicity of Cartesian Product Graphs

机译：笛卡尔积图的条件边缘故障哈密顿性

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摘要

A graph $(G)$ is conditional $(k)$-edge-fault Hamiltonian if it remains Hamiltonian after deleting at most $(k)$ edges and each vertex incident to at least two nonfaulty edges. A graph $(G)$ is $(k)$-edge-fault Hamiltonian-connected if it remains Hamiltonian-connected after deleting at most $(k)$ edges. This study shows that the conditional edge-fault Hamiltonicity of the Cartesian product network $(Gtimes H)$ can be efficiently evaluated given two graphs $(G)$ and $(H)$ that are edge-fault Hamilton-connected and conditional edge-fault Hamiltonian. This study uses the result to evaluate the conditional edge-fault Hamiltonicity of two multiprocessor systems, the generalized hypercubes and the nearest neighbor mesh hypercubes, both of which belong to Cartesian product networks.
机译：如果图形$（G）$在删除最多$（k）$条边并且每个顶点至少入射到两个无缺陷的边后仍然是哈密顿量，则它是条件$（k）$-edge-fault Hamilton。如果图形$（G）$在删除最多$（k）$边后仍保持哈密顿连通，则为$（k）$-edge-fault哈密顿连通。这项研究表明，如果给定两个图$（G）$和$（H）$分别是边缘故障的Hamilton连接和条件边缘，则可以有效地评估笛卡尔积网络$（Gtimes H）$的条件边缘故障哈密顿性故障哈密顿量。本研究使用结果评估两个多处理器系统的条件边缘故障哈密顿性，这两个多处理器系统均属于笛卡尔积网络，它们分别是广义超立方体和最近邻网格超立方体。

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