Super-connected and super-arc-connected Cartesian product of digraphs
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 delta(+)(D-i) = delta(-)(D-i) = delta(D-i) = kappa(D-i) for i = 1.2, then D-1 x D-2 is super-kappa if and only if D-1 x D-2 not congruent to D x (K) over right arrow (n) (D x (K) over right arrow (n) not congruent to (K) over right arrow (2) x (K) over right arrow (2). (K) over right arrow (2) x (K) over right arrow (3)). (ii) If delta(+)(D-i) = delta(-)(D-i) = delta(D-i) = lambda(D-i) for i = 1.2, then D-1 x D-2 is super-lambda if and only if D-1 x D-2 not congruent to D x (K) over right arrow (n). where lambda(D) = delta(D) = 1, (K) over right arrow (n) denotes the complete digraph of order n and n >= 2. (C) 2008 Elsevier B.V. All rights reserved.
super-connected super-arc-connected cartesian product combinatorial problems