| Summary: | 碩士 === 靜宜大學 === 資訊工程學系 === 102 === A graph is k-ordered hamiltonian if for every ordered set S of k vertices there exists a hamiltonian cycle which encounters S in its designated order. A graph is k-ordered hamiltonian connected if for every k ordered set S = {x_1, x_2, . . . , x_k} there exists a hamiltonian path joining x_1 to x_k that encounters S in its designated order. In this paper, we prove that the five dimensional cube-connected cycles graph, 〖CCC〗_5, is 4-ordered hamiltonian and 4-ordered hamiltonian connected graphs. This is the first non-trivial vertex transitive graph with this property.
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