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

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

doi:10.48550/arXiv.2601.17519

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

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

Research output: Working paper › Preprint › Academic

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.

Original language	English
Publisher	arXiv.org
Number of pages	36
Volume	2601.17519
DOIs	https://doi.org/10.48550/arXiv.2601.17519
Publication status	Published - 24 Jan 2026

Keywords

math.CO

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10.48550/arXiv.2601.17519

2601.17519v1Final published version, 578 KBLicence: CC BY

Cite this

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

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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AU - van de Berg, Nils

AU - Juliano, Emanuel

AU - Reijnders, Harper

AU - Simoens, Robin

AU - van Veluw, Thijs

AU - Wittebol, Jim

PY - 2026/1/24

Y1 - 2026/1/24

N2 - 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.

AB - 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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DO - 10.48550/arXiv.2601.17519

M3 - Preprint

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BT - The edge-isoperimetric number of graphs and their powers

PB - arXiv.org

ER -

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

Abstract

Keywords

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