Edge-fault-tolerant pancyclicity and bipancyclicity of Cartesian product graphs with faulty edges |
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Affiliation: | Department of Computer Science and Information Engineering, National Cheng Kung University, No. 1, University Road, Tainan 701, Taiwan |
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Abstract: | Let r≥ 4 be an even integer. Graph G is r-bipancyclic if it contains a cycle of every even length from r to , where is the number of vertices in G. A graph G is r-pancyclic if it contains a cycle of every length from r to , where . A graph is k-edge-fault Hamiltonian if, after deleting arbitrary k edges from the graph, the resulting graph remains Hamiltonian. The terms k-edge-fault r-bipancyclic and k-edge-fault r-pancyclic can be defined similarly. Given two graphs G and H, where , 9, let , be the minimum degrees of G and H, respectively. This study determined the edge-fault r-bipancyclic and edge-fault r-pancyclic of Cartesian product graph with some conditions. These results were then used to evaluate the edge-fault pancyclicity (bipancyclicity) of and . |
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Keywords: | Cartesian product graphs Edge-bipancyclic Edge-pancyclic Fault-tolerant embeddings Interconnection networks |
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