On super edge-connectivity of Cartesian product graphs

  • Authors:

  • Min Lü;Guo-Liang Chen;Jun-Ming Xu

  • 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, 23002 ...;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, 23002 ...;Department of Mathematics, University of Science and Technology of China, Hefei, Anhui, 230026, People's Republic of China

  • Venue:
  • Networks
  • Year:
  • 2007

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Abstract

The super edge-connectivity λ′ of a connected graph G is the minimum cardinality of an edge-cut F in G such that every component of G - F contains at least two vertices. Let Gi be a connected graph with order ni, minimum degree δi and edge-connectivity λi for i = 1, 2. This article shows that λ′(G1 × G2) ≥ min{n1λ2, n2λ1, λ1 + 2 λ2, 2 λ1 + λ 2} for n1, n2 ≥ 3 and λ′(K2 × G2) = min{ n2, 2λ2}, which generalizes the main result of Shieh on the super edge-connectedness of the Cartesian product of two regular graphs with maximum edge-connectivity. In particular, this article determines λ′(G1 × G2) = min{n1δ2, n2δ1, ξ{G1 × G2)} if λ′(Gi) = ξ(Gi), where ξ(G) is the minimum edge-degree of a graph G. © 2006 Wiley Periodicals, Inc. NETWORKS, Vol. 49(2), 152–157 2007