The restricted arc connectivity of Cartesian product digraphs

Arc fault tolerance of cartesian product digraphs on hyper arc connectivity

“…The cartesian product of digraphs D 1 and D 2 is the digraph D 1 × D 2 whose vertex set is V (D 1 ) × V (D 2 ) and whose arc set is the set of all pairs (x 1 , y 1 )(x 2 , y 2 ) such that either x 1 x 2 ∈ A(D 1 ) and y 1 = y 2 , or y 1 y 2 ∈ A(D 2 ) and x 1 = x 2 . In [4,[6][7][8][9][10][11], the authors introduced some results about (arc) connectivity of cartesian product of digraphs.…”

On the optimality of 3-restricted arc connectivity for digraphs and bipartite digraphs

“…In [11], Hellwig and Volkmann concluded many sufficient conditions for digraphs to be λ-optimal. Besides, sufficient conditions for digraphs to be λ ′ -optimal were also given by several authors, for example by Balbuena et al [1][2][3][4], Chen et al [5,6], Grüter and Guo [7,8], Liu and Zhang [9], Volkmann [12] and Wang and Lin [13]. However, closely related conditions for λ 3 -optimal digraphs have received little attention until recently.…”

From Graph Isoperimetric Inequality to Network Connectivity -- A New Approach

“…Thus they are more refined measures of reliability for multiprocessor systems. The restricted connectivity, super connectivity and extra connectivity of many interconnection networks have been explored [2], [3], [4], [5], [10], [11], [29], [37], [44], [51], [15], [38], [39], [40], [31], [44], [28], [41], [42], [27], [33], [35], [19], [30], [32], [50], [51], [26], [48], [23], [44], [46], [24], [9], [49], [45], [47].…”