Blas Fernandez: 2-Y-homogeneous distance-biregular graphs: State of the art and beyond

2-Y-homogeneous distance-biregular graphs: State of the art and beyond

Blas Fernandez (IMFM, Ljubljana; UP FAMNIT, Koper)

Abstract: Embark on a journey into the fascinating world of (Y, Y')-distance-biregular graphs, where intriguing mathematical challenges await! In this presentation, we will explore the essential conditions that characterize these graphs as 2-Y-homogeneous, with the ultimate goal of classifying them and providing a clear roadmap to their understanding.

Guided by subconstituent algebras and combinatorial designs—our trusted companions on this journey—we will present the current progress of this project. Along the way, we will illuminate open questions and propose inspiring conjectures, uncovering the hidden beauty and depth of these intricate combinatorial objects.