On completely regular codes with minimum eigenvalue in geometric graphs Full article
| Journal |
Discrete Mathematics
ISSN: 0012-365X , E-ISSN: 1872-681X |
||
|---|---|---|---|
| Output data | Year: 2023, Volume: 346, Number: 7, Article number : 113357, Pages count : 13 DOI: 10.1016/j.disc.2023.113357 | ||
| Tags | Completely regular code; Delsarte clique; Geometric graph; Johnson graph; Reconstruction; t-design | ||
| Authors |
|
||
| Affiliations |
|
Funding (1)
| 1 | Russian Science Foundation | 22-21-00135 |
Abstract:
We prove that any completely regular code with minimum eigenvalue in any geometric graph Γ corresponds to a completely regular code in the clique graph of Γ. 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.
Cite:
Mogilnykh I.Y.
, Vorob'ev K.V.
On completely regular codes with minimum eigenvalue in geometric graphs
Discrete Mathematics. 2023. V.346. N7. 113357 :1-13. DOI: 10.1016/j.disc.2023.113357 WOS Scopus РИНЦ OpenAlex
On completely regular codes with minimum eigenvalue in geometric graphs
Discrete Mathematics. 2023. V.346. N7. 113357 :1-13. DOI: 10.1016/j.disc.2023.113357 WOS Scopus РИНЦ OpenAlex
Dates:
| Submitted: | Jun 5, 2022 |
| Accepted: | Jan 24, 2023 |
| Published online: | Mar 1, 2023 |
| Published print: | Jul 20, 2023 |
Identifiers:
| Web of science: | WOS:000950570700001 |
| Scopus: | 2-s2.0-85149317861 |
| Elibrary: | 60872480 |
| OpenAlex: | W4322738869 |