Filters








43 Hits in 3.2 sec

A chip-firing game and Dirichlet eigenvalues

Fan Chung, Robert B. Ellis
2002 Discrete Mathematics  
The game continues until no vertex can be fired. We will give an upper bound, in terms of Dirichlet eigenvalues, for the number of firings needed before a game terminates.  ...  We consider a variation of the chip-firing game in a induced subgraph S of a graph G.  ...  After preliminary definitions in Section 2, in Section 3 we obtain a bound on the length of the Dirichlet game in terms of the number of chips and the Dirichlet eigenvalues of the graph.  ... 
doi:10.1016/s0012-365x(02)00434-x fatcat:cy4yrqp7bzamrblhi25zme6kua

Page 6549 of Mathematical Reviews Vol. , Issue 2003i [page]

2003 Mathematical Reviews  
Lass.” 2003i:05087 05C50 91443 Chung, Fan (1-UCSD; La Jolla, CA); Ellis, Robert B. (1-UCSD; La Jolla, CA) A chip-firing game and Dirichlet eigenvalues.  ...  We give an upper bound, in terms of Dirichlet eigenvalues, for the number of firings needed before a game terminates.  ... 

Page 7564 of Mathematical Reviews Vol. , Issue 98M [page]

1998 Mathematical Reviews  
One variant of the chip firing games, called the dollar game and introduced by the author, gives rise to the so-called critical configurations which may be thought of as elements in a group.  ...  A number of short proofs are included. Among the more recent results discussed in the survey are the chip firing games which relate in a natural way to the Laplacian.  ... 

Author index to volume

2002 Discrete Mathematics  
Ellis, A chip-firing game and Dirichlet eigenvalues (2-3) 341-355 Corbas, B. and G.D. Williams, Congruence classes in M 3 ðF q Þ ðq even) (1) 15-27 Cowen, L.J., J.R. Griggs and D.B.  ...  errez, A., see J.A. Rodr! ıguez (1) 101-109 Gy! arf! as, A., see Z. F . uredi (2-3) 385-403 Gy! arf! as, A., A.E. K! ezdy and J. Lehel, A finite basis characterization of a-, A. and K.  ... 
doi:10.1016/s0012-365x(02)00700-8 fatcat:hkrv7qelo5copoel65lcrt6mzi

Multi-commodity Allocation for Dynamic Demands Using PageRank Vectors [chapter]

Fan Chung, Paul Horn, Jacob Hughes
2012 Lecture Notes in Computer Science  
In this process, the demands for several types of commodities are initially given at some specified vertices and then the demands spread interactively on a contact graph.  ...  While not strictly necessary, we assume that there is a self loop at each vertex. In this case, d v includes v in the count of neighbors and hence the loop counts as 1 towards the degree.  ...  Unlike in classical chip-firing games, the number of chips is not static, and the process is continuous time. We restate the possible transitions in terms of demand chips.  ... 
doi:10.1007/978-3-642-30541-2_11 fatcat:nqrcgryd2fbgbcp3fthci33kcu

Multicommodity Allocation for Dynamic Demands Using PageRank Vectors

Fan Chung, Paul Horn, Jacob Hughes
2014 Internet Mathematics  
In this process, the demands for several types of commodities are initially given at some specified vertices and then the demands spread interactively on a contact graph.  ...  While not strictly necessary, we assume that there is a self loop at each vertex. In this case, d v includes v in the count of neighbors and hence the loop counts as 1 towards the degree.  ...  Unlike in classical chip-firing games, the number of chips is not static, and the process is continuous time. We restate the possible transitions in terms of demand chips.  ... 
doi:10.1080/15427951.2013.833148 fatcat:lunxw4giwbdy7bmmimpdz6vovu

Discrete Green's functions for products of regular graphs [article]

Robert B. Ellis
2003 arXiv   pre-print
These Green's functions may be used in conjunction with diffusion-like problems on graphs such as electric potential, random walks, and chip-firing games or other balancing games.  ...  Explicit formulas are derived for the cycle, torus, and 3-dimensional torus, as is an inductive formula for the t-dimensional torus with n vertices, from which the Green's function can be completely determined  ...  games or other balancing games.  ... 
arXiv:math/0309080v2 fatcat:slbnkp557rh4rllcbayoup5jg4

A majorization bound for the eigenvalues of some graph Laplacians [article]

Tamon Stephen
2004 arXiv   pre-print
We also show that a generalization of this conjecture to graphs with Dirichlet boundary conditions is equivalent to the original conjecture.  ...  It is conjectured that the Laplacian spectrum of a graph is majorized by its conjugate degree sequence. In this paper, we prove that this majorization holds for a class of graphs including trees.  ...  Recently [2] used the spectrum of the Dirichlet Laplacian in the analysis of "chip-firing games", which are processes on graphs that have an absorbing (Dirichlet) boundary at some vertices.  ... 
arXiv:math/0411153v1 fatcat:m52hmi7fsjbtnpee6glr3p6cym

A Majorization Bound for the Eigenvalues of Some Graph Laplacians

Tamon Stephen
2007 SIAM Journal on Discrete Mathematics  
We also show that this conjecture and its generalization to graphs with Dirichlet boundary conditions are equivalent.  ...  Grone and Merris [5] conjectured that the Laplacian spectrum of a graph is majorized by its conjugate vertex degree sequence.  ...  Recently [1] used the spectrum of the Dirichlet Laplacian in the analysis of "chip-firing games", which are processes on graphs that have an absorbing (Dirichlet) boundary at some vertices.  ... 
doi:10.1137/040619594 fatcat:loygeh7rqbfurl6apqcjil7mpu

Green functions on product networks

C. Araúz, Á. Carmona, A.M. Encinas, M. Mitjana
2019 Discrete Applied Mathematics  
and the eigenvalues and eigenfunctions of some Schrödinger operator on the other factor network.  ...  We apply our results to compute the Green function of P m × S h , where P m is a Path with m vertices and S h is a Star network with h + 1 vertices. (A.M. Encinas), margarida.mitjana@upc.edu (M.  ...  Acknowledgment This work has been supported by the Spanish Research Council, Spain, under projects MTM2014-60450-R and MTM2017-85996-R.  ... 
doi:10.1016/j.dam.2018.10.004 fatcat:mhz5f7fj35bixaulwkswy6grey

A Schur-Weyl Duality Approach to Walking on Cubes [article]

Georgia Benkart, Dongho Moon
2014 arXiv   pre-print
Walks on the representation graph R_V(G) determined by a group G and a G-module V are related to the centralizer algebras of the action of G on the tensor powers V^⊗ k via Schur-Weyl duality.  ...  We describe a basis for the centralizer algebras in terms of labeled partition diagrams.  ...  Walks on graphs are also related to chip-firing games, or to what is often referred to in physics as the (abelian) sandpile model. In a chip-firing game, each node starts with a pile of chips.  ... 
arXiv:1409.8154v2 fatcat:lss6vb4vfvfxhjoypjtodpyghy

Topic Discovery through Data Dependent and Random Projections [article]

Weicong Ding, Mohammad H. Rohban, Prakash Ishwar, Venkatesh Saligrama
2013 arXiv   pre-print
We present a suite of highly efficient algorithms based on data-dependent and random projections of word-frequency patterns to identify novel words and associated topics.  ...  This is a condition on existence of novel-words that are unique to each topic.  ...  RP chip circuit noise analog current voltage gates DDP chip circuit analog voltage pulse vlsi device Gibbs analog circuit chip output figure current vlsi RecL2 N/A RP visual cells spatial ocular  ... 
arXiv:1303.3664v2 fatcat:bvpqfxjxcza4rnf6ban7t3wzua

Diffuse Scattering on Graphs [article]

Anna C. Gilbert, Jeremy G. Hoskins, John C. Schotland
2016 arXiv   pre-print
In addition, we outline a method for finding Green's functions for Cayley graphs for both abelian and non-abelian groups.  ...  Finally, we conclude with a discussion of the effects of sparsity on our method and results, outlining the simplifications that can be made provided that the scatterers are weak and well-separated.  ...  Additionally, Green's function methods have yielded interesting results in many areas including the properties of random walks [17, 30] , chip-firing games [25] , analysis of online communities [33]  ... 
arXiv:1401.4428v2 fatcat:6dhgvhsosvdk7m7cfpnf4jahpe

Diffuse scattering on graphs

Anna C. Gilbert, Jeremy G. Hoskins, John C. Schotland
2016 Linear Algebra and its Applications  
In addition, we outline a method for finding Green's functions for Cayley graphs for both abelian and non-abelian groups.  ...  Finally, we conclude with a discussion of the effects of sparsity on our method and results, outlining the simplifications that can be made provided that the scatterers are weak and wellseparated.  ...  Additionally, Green's function methods have yielded interesting results in many areas including the properties of random walks [17, 30] , chip-firing games [25] , analysis of online communities [33]  ... 
doi:10.1016/j.laa.2016.01.012 fatcat:rk6mx57z2nhytdjfpjnvpvrziq

Page 2758 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
A chip-firing game and Dirichlet eigenvalues.  ...  of lattices induced by (extended) chip firing games.  ... 
« Previous Showing results 1 — 15 out of 43 results