|
Дискретная математика и математическая кибернетика
$L_{\infty}$ norm minimization for nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and Johnson graphs
E. A. Bespalov, I. Yu. Mogilnykh, K. V. Vorob'ev Sobolev Institute of Mathematics, pr. Koptyuga, 4, 630090, Novosibirsk, Russia
Аннотация:
We study nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and the Johnson graphs. For the first eigenvalue we obtain the minimums of the $L_{\infty}$ norm for several infinite series of Johnson graphs, including $J(n,3)$ for all $n\geq 63$, as well as general upper and lower bounds. The minimization of the $L_{\infty}$ norm for nowhere-zero integer eigenvectors with the second eigenvalue of the block graph of a Steiner triple system $S$ is equivalent to finding the minimum nowhere-zero flow for Steiner triple system $S$. For the all Assmuss-Mattson Steiner triple systems of the orders greater or equal to $99$ we prove that the minimum flow is bounded above by $5$.
Ключевые слова:
Steiner triple system, flow, strongly regular graph, Johnson graph, Grassmann graph, eigenvalue.
Поступила 3 апреля 2023 г., опубликована 21 ноября 2023 г.
Образец цитирования:
E. A. Bespalov, I. Yu. Mogilnykh, K. V. Vorob'ev, “$L_{\infty}$ norm minimization for nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and Johnson graphs”, Сиб. электрон. матем. изв., 20:2 (2023), 1125–1149
Образцы ссылок на эту страницу:
https://www.mathnet.ru/rus/semr1633 https://www.mathnet.ru/rus/semr/v20/i2/p1125
|
Статистика просмотров: |
Страница аннотации: | 50 | PDF полного текста: | 10 | Список литературы: | 14 |
|