3 ∗-Connectivity of the Fully Connected Cubic Networks

A k-container C(u, v) of G between u and v is a set of k internally disjoint paths between u and v. A k-container C(u, v) of G is a k∗-container if it contains all vertices of G. A graph G is k∗connected if there exists a k∗-container between any two distinct vertices. In this paper, we prove that the n-dimensional fully connected cubic network FCCNn is 3 ∗-connected for n ≥ 2.

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