Quadratic Embedding Constants of Strongly Regular Graphs

TL;DR

This paper derives an explicit formula for the quadratic embedding constant of strongly regular graphs and characterizes when such graphs can be embedded into Euclidean space based on this constant.

Contribution

It provides a new explicit formula for the quadratic embedding constant of strongly regular graphs and a criterion for their Euclidean embedding.

Findings

Explicit formula for QEC of strongly regular graphs

Necessary and sufficient condition for Euclidean embedding

Enhanced understanding of graph embedding properties

Abstract

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