On reconstruction of eigenfunctions of Johnson graphs
Combinatorics
2018-12-07 v1
Abstract
In the present work we consider the problem of a reconstruction of eigenfunctions of the Johnson graph . We give necessary and sufficient numerical conditions for a unique reconstruction of an eigenfunction with given eigenvalue by its values on a sphere of given radius for big enough. We also provide examples of functions equal on the sphere but not equal on the full vertex set in the case of a failure of these conditions.
Cite
@article{arxiv.1812.02424,
title = {On reconstruction of eigenfunctions of Johnson graphs},
author = {Konstantin Vorob'ev},
journal= {arXiv preprint arXiv:1812.02424},
year = {2018}
}
Comments
This paper is an extended version of the talk given by the author at the Second Russian-Hungarian Combinatorial Workshop held in Budapest, June 27-29, 2018