The Generalized 4-Connectivity of Locally Exchanged Twisted Cubes

The generalized connectivity is a generalization of the traditional connectivity. It provides a new way to measure the fault tolerance of interconnection networks. For a network G and a vertex subset S subset of V (G), kappa(G)(S) denotes the maximum integer l of edge-disjoint trees T-1,T-2,& mldr;,T-l in G such that V (T-i) boolean AND V (T-j) = S for i,j is an element of{1, 2,& mldr;,l} and i not equal j. For an integer k where 2 <= k <=|V (G)|, the generalized k-connectivity of G, denoted by kappa(k)(G), is defined as kappa(k)(G) =min{kappa(G)(S)|S subset of V (G) and |S| = k}. Locally exchanged twisted cube LeTQ(s,t) is an enhanced variant of the locally twisted cube. In this work, we obtain that kappa(4)(LeTQ(s,t)) = kappa(3)(LeTQ(s,t)) = s for 3 <= s <= t.