What type of study is this?

This is a Quantitative Study study.

October 9, 2025Open Access

Which maximal subgroups are perfect codes?

Key Points

Maximal subgroups can serve as perfect codes in certain Cayley graphs.
A perfect code requires every vertex outside the code to be adjacent to exactly one vertex in the code.
The study emphasizes characterizing subgroup perfect codes through their local complements.
Understanding perfect codes furthers knowledge of graph structures and subgroup properties.

Abstract

A perfect code in a graph Γ= (V, E) is a subset C of V such that no two vertices in C are adjacent and every vertex in V C is adjacent to exactly one vertex in C. A subgroup H of a group G is called a subgroup perfect code of G if it is a perfect code in some Cayley graph of G. In this paper, we undertake a systematic study of which maximal subgroups of a group can be perfect codes. Our approach highlights a characterization of subgroup perfect codes in terms of their ``local'' complements.

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Cite This Study

Qıao et al. (Thu,) studied this question.

synapsesocial.com/papers/68e7103b90569dd607ee6a06 https://doi.org/https://doi.org/10.48550/arxiv.2507.23635

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