THE COMPONENT REALIZABILITY OF CUBIC DECOMPOSITIONS OF ORDER 10, THAT HAVE ORDER TYPE 1021

L P Petrenjuk, A J Petrenjuk

Анотація


Продовжено дослідження кубічних розкладів порядку 10. Для типу 1021розрізнено реалізовні та нереалізовні компонентні типи. Для кожного реалізовного компонентного типу побудовано реалізуючий розклад.

More than ten years ago there was done the partition of the set of cubic decompositions o the complete graph of order 10 into 14 types [1].Under the type of the cubic decomposition R of the graph Kn we understand the vector  a(R)=(a4, a6,...), where ai means the number o components of order i in the decomposition R. The type is an invariant with regard to isomorphism in the set of cubic decompositions of order n. Such types we call the order types.


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L.P. Petrenjuk, A.J. Petrenjuk, The existence of certain types of cubic decompositions of the graph K10 (Ukrainian). The Materials of the First Inter-High-Schools Seminar “Combinatorial Configurations and Their Applications”, Kirovograd, April 19–20, 2006, 39–40.

L.P. Petrenjuk, A.J. Petrenjuk, The existence of cubic decompositions of order 10 (type 1102), The Materials of the Ninth International Science and Practice Conference “Science and Education – ‘2006”, vol. 13, Physics and Mathematics. Dnipropetrovs’k, Science and Education, 2006, 64–68.

8. L.P. Petrenjuk, A.J. Petrenjuk, On the existence of cubic decompositions of the graph K10 with the type 2011 (Ukrainian). Scientific Notes, vyp.65, Mathematical Sciences. Kirovograd State Pedagogical University, 2006, 85–94.

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D.A. Petrenjuk. On the cubic decompositions of the graph K13. The Materials of the First Inter-High-Schools Seminar “Combinatorial Configurations and Their Applications”. Kirovograd, April 19–20, 2006, 41–42.


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