Symmetry of factors of the 7-cube hamming shell
Italo Jose Dejter · Journal of Combinatorial Designs · 1997
A 1-factorization F1 of the complement Σ7 of the perfect Hamming code in the 7-cube graph Q7 is given explicitly. For i = 2, 3, the component 1-factors of F1 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. © 1997 John Wiley & Sons, Inc. J Combin Designs 5: 301–309, 1997