Series of families of degree six circulant graphs E. A. Monakhova
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ArticleContent type: Текст Media type: электронный Other title: Cерии семейств циркулянтных графов степени шесть [Parallel title]Subject(s): проблема d/k графов | семейства циркулянтных графов степени 6 | трехмерные кольцевые циркулянтные графы | экстремальные циркулянтны графы | Кэли граф абелевой группыGenre/Form: статьи в журналах Online resources: Click here to access online
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Прикладная дискретная математика № 54. С. 109-124Abstract: An approach for constructing and optimizing graphs of series of analytically described circulant graphs of degree six with general topological properties is proposed. The paper presents three series of families of undirected circulants having the form C (N (d, p); 1, s 2(d ,p ) , s 3 (d,p)), with an arbitrary diameter d > 1 and a variable parameter p(d), 1 @ p (d ) @ d. The orders N of each graph in the families are determined by a cubic polynomial function of the diameter, and generators s2 and s 3 are defined by polynomials of the diameter of various orders. We have proved that the found series of families include degree six extremal circulant graphs with the largest known orders for all diameters. By specifying the functions p(d), new infinite families of circulant graphs including solutions close to extremal graphs are obtained.
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An approach for constructing and optimizing graphs of series of analytically described circulant graphs of degree six with general topological properties is proposed. The paper presents three series of families of undirected circulants having the form C (N (d, p); 1, s 2(d ,p ) , s 3 (d,p)), with an arbitrary diameter d > 1 and a variable parameter p(d), 1 @ p (d ) @ d. The orders N of each graph in the families are determined by a cubic polynomial function of the diameter, and generators s2 and s 3 are defined by polynomials of the diameter of various orders. We have proved that the found series of families include degree six extremal circulant graphs with the largest known orders for all diameters. By specifying the functions p(d), new infinite families of circulant graphs including solutions close to extremal graphs are obtained.
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