A Note on the Critical Groups of Strongly Regular Graphs and Their Generalizations
Combinatorics
2022-09-14 v2
Abstract
We determine the maximum order of an element in the critical group of a strongly regular graph, and show that it achieves the spectral bound due to Lorenzini. We extend the result to all graphs with exactly two non-zero Laplacian eigenvalues, and study the signed graph version of the problem. We also study the monodromy pairing on the critical groups, and suggest an approach to study the structure of these groups using the pairing.
Keywords
Cite
@article{arxiv.2203.11384,
title = {A Note on the Critical Groups of Strongly Regular Graphs and Their Generalizations},
author = {Kenneth Hung and Chi Ho Yuen},
journal= {arXiv preprint arXiv:2203.11384},
year = {2022}
}
Comments
v1: 14 pages; v2: 15 pages, stronger result in Section 4 and improved exposition. To appear in Innovations in Incidence Geometry: Algebraic, Topological and Combinatorial