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An alternative construction of the $G_2(2)$-graph

Koichi Inoue

Abstract

In this note, we give an alternative construction of the $G_2(2)$-graph from a $U_3(2)$-geometry.

An alternative construction of the $G_2(2)$-graph

Abstract

In this note, we give an alternative construction of the -graph from a -geometry.
Paper Structure (6 sections, 7 theorems, 18 equations)

This paper contains 6 sections, 7 theorems, 18 equations.

Table of Contents

  1. Abstract.
  2. Keywords:
  3. Introduction
  4. Preliminaries
  5. The $G_2(2)$-graph
  6. The construction

Key Result

Lemma 2.1

The complement of a strongly regular graph with parameters $(n,k,\lambda,\mu)$ is also strongly regular graph with parameters $(n,n-k-1,n-2k+\mu-2,n-2k+\lambda)$.

Theorems & Definitions (11)

  • Lemma 2.1
  • Lemma 2.2
  • Lemma 2.3
  • Definition 4.1
  • Lemma 4.2
  • proof
  • Lemma 4.3
  • proof
  • Lemma 4.4
  • proof
  • ...and 1 more