Graduate Student Colloquium: Dorian Smith

Sandpile Groups of Cones over Bi-Coconut Trees

Sandpile groups are a subtle graph isomorphism invariant, in the form of a finite abelian group, whose cardinality is the number of spanning trees in the graph. The sandpile group of a cone over a tree has been examined by Reiner and Smith. We extend their results by determining the group structure of the sandpile group of the cone over a bi-coconut tree. It is described as follows: A bi-coconut tree graph, denoted , is obtained from a path on vertices by adding leaf vertices respectively to each endvertex of the path.

Dorian Smith
Graduate Student
University of Minnesota Twin Cities