Super-connectivity and super-edge-connectivity for some interconnection networks |
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Authors: | Y-Chuang Chen Jimmy J M Tan Lih-Hsing Hsu Shin-Shin Kao |
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Institution: | a Department of Computer and Information Science, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;b Department of Applied Mathematics, Chung-Yuan Christian University, Chong-Li City 320, Taiwan, ROC |
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Abstract: | Let G=(V,E) be a k-regular graph with connectivity κ and edge connectivity λ. G is maximum connected if κ=k, and G is maximum edge connected if λ=k. Moreover, G is super-connected if it is a complete graph, or it is maximum connected and every minimum vertex cut is {x|(v,x)E} for some vertex vV; and G is super-edge-connected if it is maximum edge connected and every minimum edge disconnecting set is {(v,x)|(v,x)E} for some vertex vV. In this paper, we present three schemes for constructing graphs that are super-connected and super-edge-connected. Applying these construction schemes, we can easily discuss the super-connected property and the super-edge-connected property of hypercubes, twisted cubes, crossed cubes, möbius cubes, split-stars, and recursive circulant graphs. |
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Keywords: | Connectivity Edge connectivity Super-connectivity Super-edge-connectivity |
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