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Mathematics of Computation

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On the enumeration of one-factorizations of complete graphs containing prescribed automorphism groups

Authors: E. Seah and D. R. Stinson
Journal: Math. Comp. 50 (1988), 607-618
MSC: Primary 05C30; Secondary 05B30, 05C45, 05C70, 20B25
MathSciNet review: 929557
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Abstract: In this paper we use orderly algorithms to enumerate (perfect) one-factorizations of complete graphs, the automorphism groups of which contain certain prescribed subgroups. We showed that, for the complete graph ${K_{12}}$, excluding those one-factorizations containing exactly one automorphism of six disjoint cycles of length two, there are precisely 56391 nonisomorphic one-factorizations of ${K_{12}}$ with nontrivial automorphism groups. We also determined that there are precisely 21 perfect one-factorizations of ${K_{14}}$ that have nontrivial automorphism groups.

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Article copyright: © Copyright 1988 American Mathematical Society