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PreprintCC BY 4.0arXiv

Spectrum of Johnson graphs

  • M. Koshelev
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Abstract

In this paper we prove new bounds on the second eigenvalue of Johnson graphs. We then apply these bounds to obtain new results on the modularity of Johnson graphs and their random subgraphs, hamiltonicity of Johnson graphs and thresholds of the appearance of the hamilton cycles and giant components. Futhermore, we provide general bounds on vertex connectivity and the stability of the modularity for $(n, d, λ)$-graphs.

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Cite

BibTeXRIS
BibTeX
@misc{koshelev2026spectrum,
  title = {{Spectrum of Johnson graphs}},
  author = {M. Koshelev},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.07887},
  eprint = {2609.07887},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.07887},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Spectrum of Johnson graphs
AU  - M. Koshelev
PY  - 2026
DA  - 2026/09/07
PB  - arXiv
DO  - 10.48550/arxiv.2609.07887
UR  - https://arxiv.org/abs/2609.07887
AB  - In this paper we prove new bounds on the second eigenvalue of Johnson graphs. We then apply these bounds to obtain new results on the modularity of Johnson graphs and their random subgraphs, hamiltonicity of Johnson graphs and thresholds of the appearance of the hamilton cycles and giant components. Futhermore, we provide general bounds on vertex connectivity and the stability of the modularity for $(n, d, λ)$-graphs.
ER  -