Among the seven known (non-degenerate) triangle-free strongly regular graphs, we prove that the Clebsch graph describes a matrix with exactly two distinct eigenvalues while five of the graphs do not. In showing that the minimum number of distinct eigenvalues of the Sims-Gewirtz graph is three, we answer a recently stated open question.
@article{arxiv.2502.05031,
title = {On the minimum number of distinct eigenvalues of triangle-free strongly regular graphs},
author = {Emily Egolf and Veronika Furst},
journal= {arXiv preprint arXiv:2502.05031},
year = {2025}
}