A two-fold cover of strongly regular graphs with spreads and association schemes of class five

TL;DR

This paper explores the structure of certain association schemes, showing how two-fold covers of strongly regular graphs with spreads lead to five-class fission schemes, enriching the understanding of graph symmetries.

Contribution

It demonstrates that two-fold covers of strongly regular graphs with spreads form five-class fission schemes of imprimitive schemes of class four, revealing new structural relationships.

Findings

Two-fold covers of strongly regular graphs with spreads produce five-class fission schemes.

The work links imprimitive association schemes of class four to more refined five-class schemes.

Provides a method to construct complex association schemes from simpler graph covers.

Abstract

We consider imprimitive association schemes of class four which are two-fold covers of strongly regular graphs with spreads. It will be shown that a two-fold cover of a strongly regular graph with a spread provides a five class fission scheme of the imprimitive scheme of class four.