The restricted arc connectivity of Cartesian product digraphs

  • Authors:

  • Xing Chen;Juan Liu;Jixiang Meng

  • Affiliations:

  • College of Mathematics and Systems Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China;College of Maths--Physics and Information Sciences, Xinjiang Normal University, Urumqi, Xinjiang 830054, PR China;College of Mathematics and Systems Sciences, Xinjiang University, Urumqi, Xinjiang 830046, PR China

  • Venue:
  • Information Processing Letters
  • Year:
  • 2009

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Abstract

For a strongly connected digraph D=(V(D),A(D)), an arc set S@?A(D) is a k-restricted arc cut if D-S has a non-trivial strongly connected component D"1 such that D-V(D"1) contains an arc. The restricted arc connectivity @l^'(D) is the minimum cardinality of all restricted arc-cuts. In this paper we prove that Cartesian product digraph D=D"1xD"2 of two strongly connected digraphs D"1 and D"2 is @l^'-connected. We also give an upper and lower bound for @l^'(D), respectively. Furthermore, we obtain that @l^'(C"m-xC"n-)=min{m,n,3} and @l^'(C"m-xK"n-)=n.