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PreprintCC BY 4.0arXiv

Subgroup Perfect Codes in Bi-Cayley Graphs

  • Masoumeh Koohestani
  • Nasrin Soltankhah
  • Mohsen Ghasemi
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Abstract

In this paper, we study perfect codes in bi-Cayley graphs, focusing on when two subgroups H and K of a group G can form a perfect code of the form H0 ∪ K1. We first consider the problem for a general group G and then examine what happens for special classes of groups, particularly abelian groups. Along the way, we obtain several results, including a necessary and sufficient condition for normal subgroups to form a perfect code, as well as an equivalent condition for abelian groups in terms of their Sylow 2-subgroups. Finally, we study the same problem for dihedral groups, providing results for this important class of non-abelian groups.

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Cite

BibTeXRIS
BibTeX
@misc{koohestani2026subgroup,
  title = {{Subgroup Perfect Codes in Bi-Cayley Graphs}},
  author = {Masoumeh Koohestani and Nasrin Soltankhah and Mohsen Ghasemi},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.16235},
  eprint = {2610.16235},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.16235},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Subgroup Perfect Codes in Bi-Cayley Graphs
AU  - Masoumeh Koohestani
AU  - Nasrin Soltankhah
AU  - Mohsen Ghasemi
PY  - 2026
DA  - 2026/10/12
PB  - arXiv
DO  - 10.48550/arxiv.2610.16235
UR  - https://arxiv.org/abs/2610.16235
AB  - In this paper, we study perfect codes in bi-Cayley graphs, focusing on when two subgroups H and K of a group G can form a perfect code of the form H_0 ∪ K_1. We first consider the problem for a general group G and then examine what happens for special classes of groups, particularly abelian groups. Along the way, we obtain several results, including a necessary and sufficient condition for normal subgroups to form a perfect code, as well as an equivalent condition for abelian groups in terms of their Sylow 2-subgroups. Finally, we study the same problem for dihedral groups, providing results for this important class of non-abelian groups.
ER  -