Skip to content
DraconiticResearch
Search Sources API
186,086 studies31 sourcesUpdated 44 min ago
PreprintCC BY-NC-ND 4.0arXiv

The integrability of sesqui-regular graphs with smallest eigenvalue at least −3

  • Qianqian Yang
  • Ruo-Lan Ding
Open at sourcePDFDOICite

Abstract

In this paper, we prove that every connected sesqui-regular graph with parameters (n,k,c), where c≥3, and with smallest eigenvalue in [−3,−2) is $1$-integrable if its valency is sufficiently large. The bound on c is optimal: for every integer t≥2, the Cartesian product of the Shrikhande graph and Kt is a connected sesqui-regular graph with parameters (16t,t+5,2) and smallest eigenvalue −3, but it is not $1$-integrable.

Related

  1. Resolving a Problem of Lv and Koolen on the Smallest Eigenvalue of Distance-Regular Graphs
    Zhen-Mu Hong, Fu-Tao Hu, Chenhui Lv
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  2. Second largest eigenvalue thresholds for the vertex-connectivity of regular graphs
    Suil O, Lukai Sui
    arXivPreprintarXiv licenceFull textCombinatorics & discrete mathematicsarXiv
  3. Phase transition for the smallest eigenvalue of high-dimensional sample correlation matrices
    Zeqin Lin, Guamgming Pan, Haozhu Zhao +1
    arXivPreprintarXiv licenceFull textProbabilityarXiv
  4. Smallest Cubic Non-1-Planar Graphs
    Sergey Pupyrev
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv
  5. On the weight distribution bound for the negative eigenvalue of polar collinearity graphs
    Sam Adriaensen, Jim Wittebol
    arXivPreprintCC BY 4.0Full textCombinatorics & discrete mathematicsarXiv

Cite

BibTeXRIS
BibTeX
@misc{yang2026integrability,
  title = {{The integrability of sesqui-regular graphs with smallest eigenvalue at least $-3$}},
  author = {Qianqian Yang and Ruo-Lan Ding},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.27700},
  eprint = {2609.27700},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.27700},
  note = {CC BY-NC-ND 4.0},
}
RIS
TY  - UNPB
TI  - The integrability of sesqui-regular graphs with smallest eigenvalue at least −3
AU  - Qianqian Yang
AU  - Ruo-Lan Ding
PY  - 2026
DA  - 2026/09/23
PB  - arXiv
DO  - 10.48550/arxiv.2609.27700
UR  - https://arxiv.org/abs/2609.27700
AB  - In this paper, we prove that every connected sesqui-regular graph with parameters (n,k,c), where c≥3, and with smallest eigenvalue in [−3,−2) is $1$-integrable if its valency is sufficiently large. The bound on c is optimal: for every integer t≥2, the Cartesian product of the Shrikhande graph and K_t is a connected sesqui-regular graph with parameters (16t,t+5,2) and smallest eigenvalue −3, but it is not $1$-integrable.
ER  -