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 B n can be embedded in a transposition graph T n 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.
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Lee, H., Sim, H., Seo, J., Kim, M. (2010). Embedding Algorithms for Bubble-Sort, Macro-star, and Transposition Graphs. In: Ding, C., Shao, Z., Zheng, R. (eds) Network and Parallel Computing. NPC 2010. Lecture Notes in Computer Science, vol 6289. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15672-4_12
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DOI: https://doi.org/10.1007/978-3-642-15672-4_12
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