English

Critical group structure from the parameters of a strongly regular graph

Combinatorics 2019-10-18 v1

Abstract

We give simple arithmetic conditions that force the Sylow pp-subgroup of the critical group of a strongly regular graph to take a specific form. These conditions depend only on the parameters (v,k,λ,μ)(v, k, \lambda, \mu) of the strongly regular graph under consideration. We give many examples, including how the theory can be used to compute the critical group of Conway's 9999-graph and to give an elementary argument that no srg(28,9,0,4)srg(28,9,0,4) exists.

Cite

@article{arxiv.1910.07686,
  title  = {Critical group structure from the parameters of a strongly regular graph},
  author = {Joshua E. Ducey and David L. Duncan and Wesley J. Engelbrecht and Jawahar V. Madan and Eric Piato and Christina S. Shatford and Angela Vichitbandha},
  journal= {arXiv preprint arXiv:1910.07686},
  year   = {2019}
}

Comments

20 pages

R2 v1 2026-06-23T11:46:09.758Z