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Abstract: We generalize a theorem of Knuth relating the oriented spanning trees of adirected graph G and its directed line graph LG. The sandpile group is anabelian group associated to a directed graph, whose order is the number oforiented spanning trees rooted at a fixed vertex. In the case when G is regularof degree k, we show that the sandpile group of G is isomorphic to the quotientof the sandpile group of LG by its k-torsion subgroup. As a corollary wecompute the sandpile groups of two families of graphs widely studied incomputer science, the de Bruijn graphs and Kautz graphs.



Author: Lionel Levine

Source: https://arxiv.org/



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