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PreprintarXiv licencearXiv

Switching graphs and designs

  • Aida Abiad
  • Dean Crnković
  • Louka Peters
  • Andrea Švob
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Abstract

Switching methods can be seen as certain local transformations that do not alter their basic parameters of a combinatorial structure. Efforts have been devoted in the literature to relate and unify the switching theories for codes and designs, and also for Hadamard matrices and graphs. The combinatorial structures we consider in this paper are graphs and designs. We show an extension of known switching method for constructing 2-designs to divisible designs, and then provide some examples of its application. Moreover, we prove several equivalences between switching methods for graphs and designs, and as a byproduct, we obtain a new switching method to obtain 2-designs.

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Cite

BibTeXRIS
BibTeX
@misc{abiad2026switching,
  title = {{Switching graphs and designs}},
  author = {Aida Abiad and Dean Crnković and Louka Peters and Andrea Švob},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20030},
  eprint = {2609.20030},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20030},
}
RIS
TY  - UNPB
TI  - Switching graphs and designs
AU  - Aida Abiad
AU  - Dean Crnković
AU  - Louka Peters
AU  - Andrea Švob
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20030
UR  - https://arxiv.org/abs/2609.20030
AB  - Switching methods can be seen as certain local transformations that do not alter their basic parameters of a combinatorial structure. Efforts have been devoted in the literature to relate and unify the switching theories for codes and designs, and also for Hadamard matrices and graphs. The combinatorial structures we consider in this paper are graphs and designs. We show an extension of known switching method for constructing 2-designs to divisible designs, and then provide some examples of its application. Moreover, we prove several equivalences between switching methods for graphs and designs, and as a byproduct, we obtain a new switching method to obtain 2-designs.
ER  -