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<p>This paper investigates the structure and properties of perfect codes and total perfect codes in generalized Cayley graphs. We first establish necessary and sufficient conditions under which a subset of a group forms a perfect code or a total perfect code in its corresponding generalized Cayley graph. Furthermore, we study the existence of subgroup perfect codes and subgroup total perfect codes. In addition, we explore the relationship between the perfect codes of generalized Cayley graphs of two groups and their direct product.</p>

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Subgroup (total) perfect codes of generalized Cayley graphs

  • 期刊论文

  • 发表日期：

    2026年1月19日

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  • Qianfen Liao,
  • Weijun Liu,
  • Yangming Li,
  • Delu Tian

摘要

This paper investigates the structure and properties of perfect codes and total perfect codes in generalized Cayley graphs. We first establish necessary and sufficient conditions under which a subset of a group forms a perfect code or a total perfect code in its corresponding generalized Cayley graph. Furthermore, we study the existence of subgroup perfect codes and subgroup total perfect codes. In addition, we explore the relationship between the perfect codes of generalized Cayley graphs of two groups and their direct product.