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Critical group structure from the parameters of a strongly regular graph

2019/10/17 by Ducey, Joshua E., Duncan, David L., Engelbrecht, Wesley J. +4
#05C50 #Combinatorics (math.CO) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.07686

Abstract

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, λ, μ) 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.

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