Edge-fault-tolerant pancyclicity and bipancyclicity of Cartesian product graphs with faulty edges

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Highlights

  • This paper showed the pancyclicity of Cartesian product graphs with faulty edges.

  • This paper showed the bipancyclicity of Cartesian product graphs with faulty edges.

  • Determining the edge-fault pancyclicity (bipancyclicity) of NQmr,,m1 efficiently.

  • Determining the edge-fault pancyclicity (bipancyclicity) of GQmr,,m1 efficiently.

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 2n(G)2, where n(G) is the number of vertices in G. A graph G is r-pancyclic if it contains a cycle of every length from r to n(G), where r3. 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 n(G), n(H) 9, let k1, k25 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 G×H with some conditions. These results were then used to evaluate the edge-fault pancyclicity (bipancyclicity) of NQmr,,m1 and GQmr,,m1.

Keywords

Cartesian product graphs
Edge-bipancyclic
Edge-pancyclic
Fault-tolerant embeddings
Interconnection networks

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This work was supported in part by the Ministry of Science and Technology, Taiwan under grant NSC 100-2628-E-006-027-MY3, and by (received funding from) the Headquarters of University Advancement at the National Cheng Kung University, which is sponsored by the Ministry of Education, Taiwan, ROC.