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Generalized Cayley graphs and perfect code

Liao Qianfen, Liu Weijun

Abstract

Perfect code in Cayley graphs and Cayley sum graphs is studied extensively in recent years. In this paper, we consider perfect code in generalized Cayley graphs.

Generalized Cayley graphs and perfect code

Abstract

Perfect code in Cayley graphs and Cayley sum graphs is studied extensively in recent years. In this paper, we consider perfect code in generalized Cayley graphs.
Paper Structure (2 sections, 19 theorems, 14 equations)

This paper contains 2 sections, 19 theorems, 14 equations.

Table of Contents

  1. Introduction
  2. Total perfect code

Key Result

Lemma 2.1

Let $S=\{s_1, \cdots, s_r\}$ be a generalized Cayley subset of $G$ induced by the involutory automorphism $\alpha$ and $X$ a subset of $G$. The following conditions are equivalent:

Theorems & Definitions (34)

  • Lemma 2.1
  • proof
  • Lemma 2.2
  • Lemma 2.3
  • Lemma 2.4
  • proof
  • Proposition 2.5
  • proof
  • Corollary 2.6
  • Remark 2.7
  • ...and 24 more