On completely regular codes with minimum eigenvalue in geometric graphs
Combinatorics
2022-12-23 v2 Information Theory
math.IT
Abstract
We prove that any completely regular code with minimum eigenvalue in any geometric graph G corresponds to a completely regular code in the clique graph of G. Studying the interrelation of these codes, a complete characterization of the completely regular codes in the Johnson graphs J(n,w) with covering radius w-1 and strength 1 is obtained. In particular this result finishes a characterization of the completely regular codes in the Johnson graphs J(n,3). We also classify the completely regular codes of strength 1 in the Johnson graphs J(n,4) with only one case for the eigenvalues left open.
Keywords
Cite
@article{arxiv.2210.11184,
title = {On completely regular codes with minimum eigenvalue in geometric graphs},
author = {I. Yu. Mogilnykh and K. V. Vorob'ev},
journal= {arXiv preprint arXiv:2210.11184},
year = {2022}
}