The Spanning Connectivity of the Burnt Pancake Graphs

Let u and v be any two distinct vertices of an undirected graph G, which is k-connected. For 1 ≤ w ≤ k, a w-container C(u, v) of a k-connected graph G is a set of w-disjoint paths joining u and v. A wcontainer C(u, v) of G is a w∗-container if it contains all the vertices of G. A graph G is w∗-connected if there exists a w∗-container between any two distinct vertices. Let κ(G) be the connectivity of G. A graph G is super spanning connected if G is i∗-connected for 1 ≤ i ≤ κ(G). In this paper, we prove that the n-dimensional burnt pancake graph Bn is super spanning connected if and only if n 2. key words: interconnection networks, Hamiltonian cycles, Hamiltonian connected, container