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arXiv · 2504.21488

New Constructions of Distance-Biregular Graphs

Blas Fernández·Ferdinand Ihringer·Sabrina Lato·Akihiro Munemasa
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Abstract

We construct a new family of distance-biregular graphs related to hyperovals and a new sporadic example of a distance-biregular graph related to Mathon's perp system. The infinite family can be explained using 2-$\bipartB$-homogeneity, while the sporadic example belongs to a generalization of a construction by Delorme. Additionally, we establish a new non-existence condition for distance-biregular graphs which, for instance, rules out the existence of a distance-biregular graph on $225+60$ vertices.

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Blas Fernández, Ferdinand Ihringer, Sabrina Lato, Akihiro Munemasa. 2026-07-10. New Constructions of Distance-Biregular Graphs. https://arxiv.org/abs/2504.21488

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