Geodesic
$L_{\infty}$ norm minimization for nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and Johnson graphs
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1125-1149

Voir la notice de l'article provenant de la source Math-Net.Ru

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 $5$.
Keywords: Steiner triple system, flow, strongly regular graph, Johnson graph, Grassmann graph, eigenvalue. 
@article{SEMR_2023_20_2_a38,
     author = {E. A. Bespalov and I. Yu. Mogilnykh and K. V. Vorob'ev},
     title = {$L_{\infty}$ norm minimization for nowhere-zero integer eigenvectors of the block graphs of {Steiner} triple systems and {Johnson} graphs},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {1125--1149},
     publisher = {mathdoc},
     volume = {20},
     number = {2},
     year = {2023},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a38/}
}
TY  - JOUR
AU  - E. A. Bespalov
AU  - I. Yu. Mogilnykh
AU  - K. V. Vorob'ev
TI  - $L_{\infty}$ norm minimization for nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and Johnson graphs
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2023
SP  - 1125
EP  - 1149
VL  - 20
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a38/
LA  - en
ID  - SEMR_2023_20_2_a38
ER  - 
%0 Journal Article
%A E. A. Bespalov
%A I. Yu. Mogilnykh
%A K. V. Vorob'ev
%T $L_{\infty}$ norm minimization for nowhere-zero integer eigenvectors of the block graphs of Steiner triple systems and Johnson graphs
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2023
%P 1125-1149
%V 20
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a38/
%G en
%F SEMR_2023_20_2_a38
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. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 20 (2023) no. 2, pp. 1125-1149. http://geodesic.mathdoc.fr/item/SEMR_2023_20_2_a38/