Embedding Algorithms for Bubble-Sort, Macro-Star, and Transposition Graphs

Abstract : Bubble-sort, macro-star, and transposition graphs are interconnection networks with the advantages of star graphs in terms of improving the network cost of a hypercube. These graphs contain a star graph as their sub-graph, and have node symmetry, maximum fault tolerance, and recursive partition properties. This study proposes embedding methods for these graphs based on graph definitions, and shows that a bubble-sort graph Bn can be embedded in a transposition graph Tn with dilation 1 and expansion 1. In contrast, a macro-star graph MS(2, n) can be embedded in a transposition graph with dilation n, but with an average dilation of 2 or under.