Super-connectivity and super-edge-connectivity for some interconnection networks

Linearly many faults in 2‐tree‐generated networks

“…When the number of faults is the smallest degree, a new concept of connectivity is necessary, since the graph may become disconnected. Thus several types of superconnectivity were introduced and examined for various classes of graphs in [4,7,9,11,12,16,20], including superconnectedness and tightly superconnectedness, where only singletons can appear in the remaining network, and restricted connectivity, where each remaining component must have a certain minimum size.…”

Super connectivity of k-regular interconnection networks

“…Then, recursively apply Theorem 2, Corollary 1, Lemma 3, and Lemma 4, AQ n,i is super connected for n + 1 6 i < 2n À 1. Case 2: i = n. AQ n,n is isomorphic to the hypercube Q n , and it is super connected [4]. Case 3: 3 6 i 6 n À 1.…”

“…Super connectivity is an extension of j and it considers the resilience of large networks [10]. The results concerning the super connectivity of the hypercubes, twisted-cubes, crossed-cubes, möbius cubes, split-stars, and recursive circulant graphs can be found in [4][5][6].…”

An efficient distributed algorithm for canonical labeling on directed split-stars

“…The directed split-stars are not only strongly connected, but, in fact, they have maximal arc-fault tolerance for connectivity and a small diameter [3][4][5]. Recently, Wang et al developed efficient distributed algorithms to obtain the unique minimum distance-k dominating sets, for k = 1, 2, and minimal feedback vertex sets on n-dimensional directed split-stars [13,14].…”