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Symmetry of factors of the 7‐cube hamming shell
Author(s) -
Dejter Italo J.
Publication year - 1997
Publication title -
journal of combinatorial designs
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.618
H-Index - 34
eISSN - 1520-6610
pISSN - 1063-8539
DOI - 10.1002/(sici)1520-6610(1997)5:4<301::aid-jcd5>3.0.co;2-j
Subject(s) - mathematics , combinatorics , transitive relation , pairwise comparison , vertex (graph theory) , hamming distance , complement (music) , hamming graph , automorphism , discrete mathematics , graph , hamming code , algorithm , statistics , decoding methods , biochemistry , complementation , gene , phenotype , block code , chemistry
A 1‐factorization F 1 of the complement Σ 7 of the perfect Hamming code in the 7‐cube graph Q 7 is given explicitly. For i = 2, 3, the component 1‐factors of F 1 can be reunited to form i ‐factorizations F i of Σ 7 $ 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