Algorithmic Aspects of the Reachability of Conflicting Chip Firing Game

2010 ◽  
pp. 359-370 ◽  
Author(s):  
Le Manh Ha ◽  
Nguyen Anh Tam ◽  
Phan Thi Ha Duong
Keyword(s):  
Chip Firing

scholarly journals On the sandpile model of modified wheels II

2020 ◽  
Vol 18 (1) ◽  
pp. 1531-1539
Author(s):  
Zahid Raza ◽  
Mohammed M. M. Jaradat ◽  
Mohammed S. Bataineh ◽  
Faiz Ullah
Keyword(s):  
Direct Product ◽  
Critical Group ◽  
Complete Structure ◽  
Sandpile Model ◽  
Cyclic Subgroups ◽  
Algebr Comb ◽  
Abelian Sandpile ◽  
Chip Firing ◽  
Sandpile Group

Abstract We investigate the abelian sandpile group on modified wheels {\hat{W}}_{n} by using a variant of the dollar game as described in [N. L. Biggs, Chip-Firing and the critical group of a graph, J. Algebr. Comb. 9 (1999), 25–45]. The complete structure of the sandpile group on a class of graphs is given in this paper. In particular, it is shown that the sandpile group on {\hat{W}}_{n} is a direct product of two cyclic subgroups generated by some special configurations. More precisely, the sandpile group on {\hat{W}}_{n} is the direct product of two cyclic subgroups of order {a}_{n} and 3{a}_{n} for n even and of order {a}_{n} and 2{a}_{n} for n odd, respectively.

scholarly journals The lattice structure of chip firing games and related models

2001 ◽  
Vol 155 (1-2) ◽  
pp. 69-82 ◽  
Author(s):  
Matthieu Latapy ◽  
Ha Duong Phan
Keyword(s):  
Lattice Structure ◽  
Chip Firing

Chip firing and the tutte polynomial

1997 ◽  
Vol 1 (1) ◽  
pp. 253-259 ◽  
Author(s):  
Criel Merino López
Keyword(s):  
Tutte Polynomial ◽  
Chip Firing

Properties of Chip-Firing Games on Complete Graphs

2014 ◽  
Vol 38 (4) ◽  
pp. 1463-1469
Author(s):  
Wei Zhuang ◽  
Weihua Yang ◽  
Lianzhu Zhang ◽  
Xiaofeng Guo
Keyword(s):  
Complete Graphs ◽  
Chip Firing

scholarly journals Chip firing and all-terminal network reliability bounds

2009 ◽  
Vol 6 (4) ◽  
pp. 436-445 ◽  
Author(s):  
Jason I. Brown ◽  
Charles J. Colbourn ◽  
Richard J. Nowakowski
Keyword(s):  
Network Reliability ◽  
Reliability Bounds ◽  
Chip Firing

scholarly journals Parallel chip firing games on graphs

1992 ◽  
Vol 92 (2) ◽  
pp. 291-300 ◽  
Author(s):  
Javier Bitar ◽  
Eric Goles
Keyword(s):  
Games On Graphs ◽  
Chip Firing
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