Name
Abstract | ||
|---|---|---|
The Jacobian of a graph, also known as the Picard group, sandpile group, or critical group, is a discrete analogue of the Jacobian of an algebraic curve. It is known that the order of the Jacobian of a graph is equal to its number of spanning trees, but the exact structure is known for only a few classes of graphs. In this paper, we compute the Jacobian for graphs of the form K"n@?E(H) where H is a subgraph of K"n on n-1 vertices that is either a cycle, or a union of two disjoint paths. We also offer a combinatorial proof of a result of Christianson and Reiner that describes the Jacobian for a subclass of threshold graphs. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1016/j.ejc.2011.04.003 | Eur. J. Comb. |
Keywords | Field | DocType |
threshold graph,algebraic curve,form k,sandpile group,discrete analogue,critical group,exact structure,picard group,combinatorial proof,disjoint path,spanning tree | Discrete mathematics,Combinatorics,Indifference graph,Picard group,Tree (graph theory),Chordal graph,Combinatorial proof,Cograph,Pathwidth,Pancyclic graph,Mathematics | Journal |
Volume | Issue | ISSN |
32 | 8 | 0195-6698 |
Citations | PageRank | References |
1 | 0.39 | 2 |
Authors | ||
2 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Serguei Norine | 1 | 181 | 20.90 |
| Peter Whalen | 2 | 14 | 2.42 |