Abstract: 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∞ norm for several in nite series of Johnson graphs, including J(n, 3) for all n ≥ 63, as well as general upper and lower bounds. The minimization of the L∞ 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.

Cite: Bespalov E.A. , Mogilnykh I.Y. , Vorob’ev K.V.
L∞ norm minimization problems for nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and Johnson graphs
Сибирские электронные математические известия (Siberian Electronic Mathematical Reports). 2023. V.20. N2. P.1125-1149. DOI: 10.33048/semi.2023.20.070 WOS Scopus РИНЦ

Dates:

Submitted:	Apr 3, 2023
Accepted:	Oct 9, 2023
Published print:	Nov 21, 2023
Published online:	Nov 21, 2023

Identifiers:

Web of science:	WOS:001102183400001
Scopus:	2-s2.0-85179944524
Elibrary:	82134656

Citing: Пока нет цитирований

Altmetrics: