Symmetry of factors of the 7-cube hamming shell

✍ Scribed by Italo J. Dejter

• Book ID: 101295312
• Publisher: John Wiley and Sons
• Year: 1997
• Tongue: English
• Weight: 245 KB
• Volume: 5
• Category: Article
• ISSN: 1063-8539
• DOI: 10.1002/(sici)1520-6610(1997)5:4<301::aid-jcd5>3.0.co;2-j

✦ Synopsis

A 1-factorization F1 of the complement Σ7 of the perfect Hamming code in the 7cube 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.