L∞ NORM MINIMIZATION FOR NOWHERE-ZERO INTEGER EIGENVECTORS OF THE BLOCK GRAPHS OF STEINER TRIPLE SYSTEMS AND JOHNSON GRAPHS

被引：0

作者：

Bespalov, Evgeny Andreevich ^{[1
]}

Mogilnykh, Ivan Yurevich ^{[1
]}

Vorob'ev, Konstantin Vasil'evich ^{[1
]}

机构：

[1] Sobolev Inst Math, Pr Koptyuga 4, Novosibirsk 630090, Russia

来源：

SIBERIAN ELECTRONIC MATHEMATICAL REPORTS-SIBIRSKIE ELEKTRONNYE MATEMATICHESKIE IZVESTIYA | 2023年 / 20卷 / 02期

基金：

俄罗斯科学基金会;

关键词：

Steiner triple system; flow; strongly regular graph; Johnson graph; Grassmann graph; eigenvalue; SUM FLOWS;

D O I：

10.33048/semi.2023.20.070

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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-infinity norm for several infinite 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-infinity 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.

引用

页码：1125 / 1149

页数：25