On the sandpile group of the square cycle
β Scribed by Yaoping Hou; Chingwah Woo; Pingge Chen
- Publisher
- Elsevier Science
- Year
- 2006
- Tongue
- English
- Weight
- 152 KB
- Volume
- 418
- Category
- Article
- ISSN
- 0024-3795
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π SIMILAR VOLUMES
The group of recurrent configurations in the sandpile model, introduced by Dhar [7], may be considered as a finite abelian group associated with any graph G; we call it the sandpile group of G. The aim of this paper is to prove that the sandpile group of planar graph is isomorphic to that of its dua
The square of a path (cycle) is the graph obtained by joining every pair of vertices of distance two in the path (cycle). Let \(G\) be a graph on \(n\) vertices with minimum degree \(\delta(G)\). Posa conjectured that if \(\delta(G) \geqslant \frac{2}{3} n\), then \(G\) contains the square of a hami