Comparison of two techniques for proving nonexistence of strongly regular graphs

TL;DR

This paper compares two mathematical techniques for proving the nonexistence of certain strongly regular graphs, showing that counting closed walks offers no advantage over eigenvalue multiplicity methods.

Contribution

It demonstrates that counting closed walks does not provide additional nonexistence results beyond eigenvalue multiplicity analysis for strongly regular graphs.

Findings

Counting closed walks does not rule out new parameter sets.

Eigenvalue multiplicity method is as effective as counting closed walks.

No new nonexistence results are obtained by the closed walk method.

Abstract

We show that the method of counting closed walks in strongly regular graphs rules out no parameter sets other than those ruled out by the method of counting eigenvalue multiplicities.