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Quadratic Embedding Constants of Strongly Regular Graphs

Nobuaki Obata

Abstract

We obtain an explicit formula for the quadratic embedding constant (QEC) of a strongly regular graph $\mathrm{srg}(n,k,λ,μ)$ with $μ\ge1$. By using QEC we give a necessary and sufficient condition for a strongly regular graph to admit a quadratic embeddingin a Euclidean space.

Quadratic Embedding Constants of Strongly Regular Graphs

Abstract

We obtain an explicit formula for the quadratic embedding constant (QEC) of a strongly regular graph with . By using QEC we give a necessary and sufficient condition for a strongly regular graph to admit a quadratic embeddingin a Euclidean space.
Paper Structure (6 sections, 17 theorems, 51 equations)

This paper contains 6 sections, 17 theorems, 51 equations.

Table of Contents

  1. Introduction
  2. Strongly Regular Graphs
  3. Adjacency Matrices
  4. Distance Matrices
  5. Quadratic Embedding Constants
  6. Examples

Key Result

Theorem 1.1

Let $G=\mathrm{srg}(n,k,\lambda,\mu)$ be a strongly regular graph with $\mu\ge1$. Then we have

Theorems & Definitions (38)

  • Theorem 1.1
  • Theorem 1.2
  • Theorem 1.3
  • Remark 2.1
  • Remark 2.2
  • Proposition 2.3
  • Proposition 2.4
  • Proposition 2.5
  • Proposition 2.6
  • Remark 2.7
  • ...and 28 more