On super connectivity of Cartesian product graphs

  • Authors:

  • Min Lü;Chao Wu;Guo-Liang Chen;Cheng Lv

  • Affiliations:

  • Anhui Province-Most Key Co-Lab of High Performance Computing and Its Applications, Department of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China;Anhui Province-Most Key Co-Lab of High Performance Computing and Its Applications, Department of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China;Anhui Province-Most Key Co-Lab of High Performance Computing and Its Applications, Department of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China;Department of Mathematics and Physics, Anhui Institute of Architecture and Industry, Hefei, Anhui, China

  • Venue:
  • Networks
  • Year:
  • 2008

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Abstract

The super connectivity κ1 of a connected graph G is the minimum number of vertices whose deletion results in a disconnected graph without isolated vertices; this is a more refined index than the connectivity parameter κ. This article provides bounds for the super connectivity κ1 of the Cartesian product of two connected graphs, and thus generalizes the main result of Shieh on the super connectedness of the Cartesian product of two regular graphs with maximum connectivity. Particularly, we determine that κ1(Km × Kn) = min{m + 2n - 4, 2m + n - 4} for m + n ≥ 6 and state sufficient conditions to guarantee κ1(K2 × G) = 2κ(G). As a consequence, we immediately obtain the super connectivity of the n-cube for n ≥ 3. © 2008 Wiley Periodicals, Inc. NETWORKS, 2008