Chip-Firing and the Critical Group of a Graph
Journal of Algebraic Combinatorics: An International Journal
The number of spanning trees of plane graphs with reflective symmetry
Journal of Combinatorial Theory Series A
Enumerating spanning trees of graphs with an involution
Journal of Combinatorial Theory Series A
Enumeration of spanning trees of graphs with rotational symmetry
Journal of Combinatorial Theory Series A
Unhooking circulant graphs: a combinatorial method for counting spanning trees and other parameters
WG'04 Proceedings of the 30th international conference on Graph-Theoretic Concepts in Computer Science
Chip-firing games, potential theory on graphs, and spanning trees
Journal of Combinatorial Theory Series A
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In this paper we consider the critical group of finite connected graphs which admit harmonic actions by the dihedral group D"n. In particular, we show that if the orbits of the D"n-action all have either n or 2n points then the critical group of such a graph can be decomposed in terms of the critical groups of the quotients of the graph by certain subgroups of the automorphism group. This is analogous to a theorem of Kani and Rosen which decomposes the Jacobians of algebraic curves with a D"n-action.