The super connectivity of the pancake graphs and the super laceability of the star graphs

  • Authors:

  • Cheng-Kuan Lin;Hua-Min Huang;Lih-Hsing Hsu

  • Affiliations:

  • Department of Mathematics, National Central University, Chung-Li, Taiwan, ROC;Department of Mathematics, National Central University, Chung-Li, Taiwan, ROC;Information Engineering Department, Ta Hwa Institute of Technology, Hsinchu, Taiwan, ROC

  • Venue:
  • Theoretical Computer Science
  • Year:
  • 2005

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Abstract

A k-container C(u, v) of a graph G is a set of k-disjoint paths joining u to v. A k-container C(u, v) of G is a k*-container if it contains all the vertices of G. A graph G is k*-connected if there exists a k*-container between any two distinct vertices. Let κ(G) be the connectivity of G. A graph G is super connected if G is i*-connected for all 1 ≤ i ≤ κ(G). A bipartite graph G is k*-laceable if there exists a k*-container between any two vertices from different parts of G. A bipartite graph G is super laceable if G is i*-laceable for all 1 ≤ i ≤ κ(G). In this paper, we prove that the n-dimensional pancake graph Pn is super connected if and only if n ≠ 3 and the n-dimensional star graph Sn is super laceable if and only if n ≠ 3.