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PreprintCC BY 4.0arXiv

Secure Domination in Odd-order Sierpinski Graphs

  • Qingcheng Zeng
  • Yumei Xue
  • Cheng Zeng
  • Dehui Wang
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Abstract

A nonempty vertex set D of a graph is secure if and only if, for every nonempty subset X of D, the closed neighborhood of X contains at least as many vertices of D as vertices outside D. A secure dominating set is a set that is both secure and dominating, and the secure domination number is the minimum cardinality of such a set. Previous work determined the secure domination number of Sierpinski graphs S_n k for even k and for odd k when n = 2. The exact values for odd k and n\geq3 remained open. In this paper, we determine these remaining values.

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Cite

BibTeXRIS
BibTeX
@misc{zeng2026secure,
  title = {{Secure Domination in Odd-order Sierpinski Graphs}},
  author = {Qingcheng Zeng and Yumei Xue and Cheng Zeng and Dehui Wang},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.28222},
  eprint = {2610.28222},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.28222},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Secure Domination in Odd-order Sierpinski Graphs
AU  - Qingcheng Zeng
AU  - Yumei Xue
AU  - Cheng Zeng
AU  - Dehui Wang
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2610.28222
UR  - https://arxiv.org/abs/2610.28222
AB  - A nonempty vertex set D of a graph is secure if and only if, for every nonempty subset X of D, the closed neighborhood of X contains at least as many vertices of D as vertices outside D. A secure dominating set is a set that is both secure and dominating, and the secure domination number is the minimum cardinality of such a set. Previous work determined the secure domination number of Sierpinski graphs S_n k for even k and for odd k when n = 2. The exact values for odd k and n\geq3 remained open. In this paper, we determine these remaining values.
ER  -