Mutually independent bipanconnected property of hypercube

Rooted level-disjoint partitions of Cartesian products

“…They also proved that for any set of n − 1 distinct pairs of adjacent vertices, Q n contains n − 1 mutually independent Hamiltonian paths with these pairs of vertices as endvertices. Mutually independent Hamiltonian paths and cycles in hypercubes with faulty edges were considered in [8,9,12,15,17]. Beside hypercubes this concept was also considered for wrapped butterfly graphs [11], 2-torus graphs with odd number of vertices [18], k-ary n-cubes with k being odd [10], and also in star-networks [13].…”