Symmetry of Factors of the 7-Cube Hamming Shell
نویسنده
چکیده
A 1-factorization F1 of the complement Σ7 of the perfect Hamming code in the 7cube graphQ7 is given explicitly. For i = 2, 3, the component 1-factors ofF1 can be reunited to form i-factorizations Fi of Σ7 for which the component i-factors are pairwise isomorphic. The smallest connected factors that can be obtained as edge-subset unions from factors of these two factorizations show differing transitivity behaviors: edge-transitivity versus vertex-transitivity. Moreover, the automorphism groups of these connected factors possess also differing behaviors: equality versus proper containment. c © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 301–309, 1997
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