Abstract
The connectivity and its generalizations have been well studied due to their impact on the fault tolerance and diagnosability of the interconnection networks. In this paper, we introduce a novel generalized connectivity, which combines the h-extra connectivity and r-component connectivity. Given a connected graph G=(V,E), for any h≥0 and r≥2, an h-extra r-component cut of G is a subset S⊆V such that there are at least r components in G∖S and each component has at least h+1 vertices; h-extra r-component connectivity of G, denoted as cκrh(G), is the minimum size of any h-extra r-component cut of G. We determine the h-extra r-component connectivity of n-dimensional hypercube Qn, cκr1(Qn)=2(r−1)(n−r+1) for r∈{2,3,4}.
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