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arXiv · 2602.18621

The Sandpile Group of a Cone Over a Bi-Coconut Tree

Dorian Smith
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Abstract

The sandpile group of a connected graph is a finite abelian group whose cardinality is the number of spanning trees in the graph. We compute the spanning tree number and sandpile group structure for the cone over a bi-coconut tree, generalizing work of Reiner and Smith on the cone over a coconut tree. We also answer one of their questions, by exhibiting a family of trees whose sandpile groups are all cyclic but their number of leaves grows without bound.

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Dorian Smith. 2026-02-20. The Sandpile Group of a Cone Over a Bi-Coconut Tree. https://arxiv.org/abs/2602.18621

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