Super-connectivity and super-edge-connectivity for some interconnection networks

  • Authors:

  • Y-Chuang Chen;Jimmy J. M. Tan;Lih-Hsing Hsu;Shin-Shin Kao

  • Affiliations:

  • Department of Computer and Information Science, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;Department of Computer and Information Science, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;Department of Computer and Information Science, National Chiao Tung University, Hsinchu 300, Taiwan, ROC;Department of Applied Mathematics, Chung-Yuan Christian University, Chong-Li City 320, Taiwan, ROC

  • Venue:
  • Applied Mathematics and Computation
  • Year:
  • 2003

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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 = κ. 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 v ∈ V; 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 v ∈ V. 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.