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The strongly regular twisted $D_{5,5}(q)$ graph

Ferdinand Ihringer

Abstract

We construct a new family of strongly regular graphs with the same parameters as the strongly regular graphs $D_{5,5}(q)$. The construction can be seen as a variant of the construction of twisted Grassmann graphs by Van Dam and Koolen.

The strongly regular twisted $D_{5,5}(q)$ graph

Abstract

We construct a new family of strongly regular graphs with the same parameters as the strongly regular graphs . The construction can be seen as a variant of the construction of twisted Grassmann graphs by Van Dam and Koolen.
Paper Structure (7 sections, 6 theorems, 1 equation)

This paper contains 7 sections, 6 theorems, 1 equation.

Table of Contents

  1. Introduction
  2. Twisted Grassmann graphs
  3. Changing vertices
  4. Changing edges
  5. Twisted rank 5 hyperbolic spaces
  6. Changing vertices
  7. Changing edges

Key Result

Theorem 1.1

Let $q$ be a prime power. The strongly regular graph $D_{5,5}(q)$ is not determined by its parameters.

Theorems & Definitions (10)

  • Theorem 1.1
  • Lemma 3.2
  • proof
  • Proposition 3.3
  • proof
  • Lemma 3.4
  • proof
  • Lemma 3.5
  • proof
  • Proposition 3.6