Embedding Starlike Trees into Hypercube-Like Interconnection Networks

Abstract. A starlike tree (or a quasistar) is a subdivision of a star tree. A family of hypercube-like interconnection networks called restricted HLgraphs includes many interconnection networks proposed in the literature such as twisted cubes, crossed cubes, multiply twisted cubes, Möbius cubes, Mcubes, and generalized twisted cubes. We show in this paper that every starlike tree of degree at most m with 2 m vertices is a spanning tree of m-dimensional restricted HL-graphs. It is also proved that in an mdimensional restricted HL-graph, there exist k( ≤ m − 1) vertex-disjoint si-paths with li vertices each that cover all the vertices in the graph for any k sources s1, s2,..., sk associated with positive integers l1, l2,..., lk whose sum is equal to the number of vertices