Critical group structure from the parameters of astrongly regular graph

JOURNAL OF COMBINATORIAL THEORY SERIES A

卷:180

Article

Ducey, Joshua E.¹  Duncan, David L.¹  Engelbrecht, Wesley J.¹  Madan, Jawahar, V²  Piato, Eric³  Shatford, Christina S.⁴  Vichitbandha, Angela⁵ 

[1] James Madison Univ, Dept Math & Stat, Harrisonburg, VA 22807 USA

[2] Harvey Mudd Coll, Dept Math, Claremont, CA 91711 USA

[3] SUNY Coll Geneseo, Dept Math, Geneseo, NY 14454 USA

[4] Connecticut Coll, Math & Stat Dept, New London, CT 06320 USA

[5] Univ Kentucky, Dept Math, Lexington, KY 40506 USA

关键词: Invariant factors;    Elementary divisors;    Smith normal form;    Critical group;    Jacobian group;    Sandpile group;    Laplacian matrix;    Strongly regular graph;    99-graph;    Moore graph;   

DOI  :  10.1016/j.jcta.2021.105424

来源: Elsevier

【 摘 要 】

We give simple arithmetic conditions that force the Sylow p-subgroup of the critical group of a strongly regular graph to take a specific form. These conditions depend only on the parameters (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 99-graph and to give an elementary argument that no srg(28, 9, 0, 4) exists. (C) 2021 Elsevier Inc. All rights reserved.

【 授权许可】

Free