| Summary: | 碩士 === 中原大學 === 應用數學研究所 === 98 === An interconnection network connects the processors of a parallel computer. It is possible that
processors and communication links fail in any interconnection network. Suppose a graph, which
represents an interconnection network, is proved to be "highly" fault-tolerant. It will be desir-
able if there exists a simple method to "expand" the graph such that it not only accommodates
more vertices and edges but also remains highly fault-tolerant after expanding. In this paper, we
propose two construction schemes for 4-regular 2-hamiltonian graphs, the "4-join" and the "cycle
extension". We show that the expanded graph misses the fault tolerance after the 4-join scheme,
but remains fault-tolerant after the cycle extension.
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