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arXiv · 2601.17519

The edge-isoperimetric number of graphs and their powers: approaches from spectral graph theory, optimization and finite geometry

Aida Abiad·Nils van de Berg·Emanuel Juliano·Harper Reijnders·Robin Simoens·Thijs van Veluw·Jim Wittebol
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Abstract

We obtain several sharp spectral bounds, approximations, and exact values for the isoperimetric number and related edge-expansion parameters of graphs. Our results focus on graph powers and on families of graphs with rich algebraic or geometric structure, including distance-regular graphs and graphs arising from finite geometries, among others. Our proofs use techniques from spectral graph theory, linear optimization, finite geometry, and probability, yielding new machinery for analysing edge-expansion phenomena in highly structured graphs.

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Aida Abiad, Nils van de Berg, Emanuel Juliano, Harper Reijnders, Robin Simoens, Thijs van Veluw, Jim Wittebol. 2026-01-24. The edge-isoperimetric number of graphs and their powers: approaches from spectral graph theory, optimization and finite geometry. https://arxiv.org/abs/2601.17519

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