Existence of strongly regular graphs with feasible parameter sets

Determine for which feasible parameter quadruples $(n,k,\lambda,\mu)$ a strongly regular graph exists, including parameter sets whose existence or non-existence remains unresolved.

Background

The paper recalls that strongly regular graphs are specified by parameters (n,k,λ,μ)(n,k,\lambda,\mu) satisfying necessary algebraic conditions. Although many parameter sets have been classified as realizable or impossible, a substantial collection remains unresolved. The existence problem is a central issue in the theory of strongly regular graphs and motivates the paper’s applications of clique graphs to unknown examples.

References

One of the biggest questions on the topic of strongly regular graphs is for which sets of parameters ($n,k,\lambda,\mu$) does a strongly regular graph exist. A large list of feasible parameter sets can be found on Andries Brouwer's website . Brouwer's list categorizes each set of srg parameters into three groups (existence, non-existence, and unknown).

— On Clique Graphs and Clique Regular Graphs  (2502.17845 - Petro et al., 25 Feb 2025) in Section 2.2, Strongly Regular Graphs