On the Enumeration of One-Factorizations of Complete Graphs Containing Prescribed Automorphism Groups
نویسندگان
چکیده
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 Ki2, excluding those one-factorizations containing exactly one automorphism of six disjoint cycles of length two, there are precisely 56391 nonisomorphic one-factorizations of Ki2 with nontrivial automorphism groups. We also determined that there are precisely 21 perfect one-factorizations of Ku that have nontrivial automorphism groups.
منابع مشابه
There are 1,132,835,421,602,062,347 nonisomorphic one-factorizations of K14
We establish by means of a computer search that a complete graph on 14 vertices has 98,758,655,816,833,727,741,338,583,040 distinct and 1,132,835,421,602,062,347 nonisomorphic one-factorizations. The enumeration is constructive for the 10,305,262,573 isomorphism classes that admit a nontrivial automorphism.
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