An explicit formula for the sandpile group of polygon flower graphs is derived from spanning tree numbers of the component chains and their contractions, plus a condition for the group to be cyclic.
The Sandpile Group of a Thick Cycle Graph
1 Pith paper cite this work. Polarity classification is still indexing.
1
Pith paper citing it
abstract
The majority of graphs whose sandpile groups are known are either regular or simple. We give an explicit formula for a family of non-regular multi-graphs called thick cycles. A thick cycle graph is a cycle where multi-edges are permitted. Its sandpile group is the direct sum of cyclic groups of orders given by quotients of greatest common divisors of minors of its Laplacian matrix. We show these greatest common divisors can be expressed in terms of monomials in the graph's edge multiplicities.
fields
math.CO 1years
2019 1verdicts
UNVERDICTED 1representative citing papers
citing papers explorer
-
The sandpile group of a polygon flower
An explicit formula for the sandpile group of polygon flower graphs is derived from spanning tree numbers of the component chains and their contractions, plus a condition for the group to be cyclic.