Combinatorial Designs, Difference Sets, and Bent Functions as Perfect Colorings of Graphs and Multigraphs Full article
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Siberian Mathematical Journal
ISSN: 0037-4466 , E-ISSN: 1573-9260 |
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| Output data | Year: 2020, Volume: 61, Number: 5, Pages: 867-877 Pages count : 11 DOI: 10.1134/s0037446620050109 | ||
| Tags | perfect coloring, transversals of a hypergraph, combinatorial designs, q-analogs of combinatorial designs, difference sets, bent functions, Johnson graph, Grassmann graph, Delsarte-Hoffman bound. | ||
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Abstract:
We prove that (1): the characteristic function of each independent set in each regular graph attaining the Delsarte–Hoffman bound is a perfect coloring; (2): each transversal in a uniform regular hypergraph is an independent set in the vertex adjacency multigraph of a hypergraph attaining the Delsarte-Hoffman bound for this multigraph; and (3): the combinatorial designs with parameters t-(v,k,λ) and their q-analogs, difference sets, Hadamard matrices, and bent functions are equivalent to perfect colorings of some graphs of multigraphs, in particular, the Johnson graph J(n,k) for (k-1)-(v,k,λ)-designs and the Grassmann graph J2(n,2) for bent functions.
Cite:
Potapov V.N.
, Avgustinovich S.V.
Combinatorial Designs, Difference Sets, and Bent Functions as Perfect Colorings of Graphs and Multigraphs
Siberian Mathematical Journal. 2020. V.61. N5. P.867-877. DOI: 10.1134/s0037446620050109 WOS Scopus РИНЦ OpenAlex
Combinatorial Designs, Difference Sets, and Bent Functions as Perfect Colorings of Graphs and Multigraphs
Siberian Mathematical Journal. 2020. V.61. N5. P.867-877. DOI: 10.1134/s0037446620050109 WOS Scopus РИНЦ OpenAlex
Original:
Потапов В.Н.
, Августинович С.В.
Комбинаторные дизайны, разностные множества и бент-функции как совершенные раскраски графов и мультиграфов
Сибирский математический журнал. 2020. Т.61. №5. С.1087-1100. DOI: 10.33048/smzh.2020.61.510 РИНЦ OpenAlex
Комбинаторные дизайны, разностные множества и бент-функции как совершенные раскраски графов и мультиграфов
Сибирский математический журнал. 2020. Т.61. №5. С.1087-1100. DOI: 10.33048/smzh.2020.61.510 РИНЦ OpenAlex
Dates:
| Submitted: | Feb 18, 2020 |
| Accepted: | Apr 8, 2020 |
Identifiers:
| Web of science: | WOS:000573304200010 |
| Scopus: | 2-s2.0-85091628704 |
| Elibrary: | 45290742 |
| OpenAlex: | W3090986818 |