Super-connected and super-arc-connected Cartesian product of digraphs

Authors:
Juan Liu;Jixiang Meng
Affiliations:
College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P.R. China;College of Mathematics and System Sciences, Xinjiang University, Urumqi, Xinjiang 830046, P.R. China
Venue:
Information Processing Letters
Year:
2008

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Abstract

We study the super-connected, hyper-connected and super-arc-connected Cartesian product of digraphs. The following two main results will be obtained:(i)If @d^+(D"i)=@d^-(D"i)=@d(D"i)=@k(D"i) for i=1,2, then D"1xD"2 is super-@k if and only if D"1xD"2@?DxK"n-(DxK"n-@?K"2-xK"2-,K"2-xK"3-), (ii)If @d^+(D"i)=@d^-(D"i)=@d(D"i)=@l(D"i) for i=1,2, then D"1xD"2 is super-@l if and only if D"1xD"2@?DxK"n-, where @l(D)=@d(D)=1, K"n- denotes the complete digraph of order n and n=2.