In this note, we describe a construction that leads to families of graphs whose critical groups are cyclic. For some of these families we are able to give a formula for the number of spanning trees of the graph, which then determines the group exactly.
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Becker, Ryan P., and Darren B. Glass. "Cyclic Critical Groups of Graphs." The Australasian Journal of Combinatorics 64.1 (February 2016), 366-375.
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