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PreprintarXiv licencearXiv

The v-number of t-closed neighborhood ideals

  • Delio Jaramillo-Velez
  • Hiram H. López
  • Rodrigo San-José
  • Nart Shalqini
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Abstract

We give a combinatorial characterization of the v-number of a t-closed neighborhood ideal associated to a graph G, and investigate its relation with other invariants such as the t-domination number and the smallest size of a ball of radius t in the graph G. We present several new cases where it is satisfied that the v-number is bounded above by the Castelnuovo-Mumford regularity. We analyze the behavior of the v-number of a t-closed neighborhood ideal with respect to the parameter t. Lastly, we compute explicit formulas for the v-number in the case of paths, cycles, and caterpillars, and analyze the case of Hamming graphs.

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Cite

BibTeXRIS
BibTeX
@misc{jaramillovelez2026vnumber,
  title = {{The $\rmv$-number of $t$-closed neighborhood ideals}},
  author = {Delio Jaramillo-Velez and Hiram H. López and Rodrigo San-José and Nart Shalqini},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.33858},
  eprint = {2610.33858},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.33858},
}
RIS
TY  - UNPB
TI  - The v-number of t-closed neighborhood ideals
AU  - Delio Jaramillo-Velez
AU  - Hiram H. López
AU  - Rodrigo San-José
AU  - Nart Shalqini
PY  - 2026
DA  - 2026/10/24
PB  - arXiv
DO  - 10.48550/arxiv.2610.33858
UR  - https://arxiv.org/abs/2610.33858
AB  - We give a combinatorial characterization of the v-number of a t-closed neighborhood ideal associated to a graph G, and investigate its relation with other invariants such as the t-domination number and the smallest size of a ball of radius t in the graph G. We present several new cases where it is satisfied that the v-number is bounded above by the Castelnuovo-Mumford regularity. We analyze the behavior of the v-number of a t-closed neighborhood ideal with respect to the parameter t. Lastly, we compute explicit formulas for the v-number in the case of paths, cycles, and caterpillars, and analyze the case of Hamming graphs.
ER  -