On the sandpile group of the graph K3 × Cn

Yaoping Hou; Tiangang Lei; Chingwah Woo

doi:10.1016/j.laa.2007.10.033

On the sandpile group of the graph K₃ × C_n

Yaoping Hou
, Tiangang Lei
, Chingwah Woo

Department of Mathematics

Research output: Journal Publications and Reviews › RGC 21 - Publication in refereed journal › peer-review

13 Citations (Scopus)

Abstract

The sandpile group of a graph is a refinement of the number of spanning trees of the graph and is closely connected with the graph Laplacian matrix. In this paper, the structure of the sandpile group on the graph K₃ × C_n is determined and it is shown that the Smith normal form of the sandpile group of K₃ × C_n is always the direct sum of four or five cyclic groups. Our methods can be generated to the graphs K₄ × C_n and K₅ × C_n. © 2007 Elsevier Inc. All rights reserved.

Original language	English
Pages (from-to)	1886-1898
Journal	Linear Algebra and Its Applications
Volume	428
Issue number	8-9
DOIs	https://doi.org/10.1016/j.laa.2007.10.033
Publication status	Published - 15 Apr 2008

Research Keywords

Critical group
Cycle
Graph Laplacian
Sandpile group
The Smith normal form

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abstract = "The sandpile group of a graph is a refinement of the number of spanning trees of the graph and is closely connected with the graph Laplacian matrix. In this paper, the structure of the sandpile group on the graph K3 × Cn is determined and it is shown that the Smith normal form of the sandpile group of K3 × Cn is always the direct sum of four or five cyclic groups. Our methods can be generated to the graphs K4 × Cn and K5 × Cn. {\textcopyright} 2007 Elsevier Inc. All rights reserved.",

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T1 - On the sandpile group of the graph K3 × Cn

AU - Hou, Yaoping

AU - Lei, Tiangang

AU - Woo, Chingwah

PY - 2008/4/15

Y1 - 2008/4/15

N2 - The sandpile group of a graph is a refinement of the number of spanning trees of the graph and is closely connected with the graph Laplacian matrix. In this paper, the structure of the sandpile group on the graph K3 × Cn is determined and it is shown that the Smith normal form of the sandpile group of K3 × Cn is always the direct sum of four or five cyclic groups. Our methods can be generated to the graphs K4 × Cn and K5 × Cn. © 2007 Elsevier Inc. All rights reserved.

AB - The sandpile group of a graph is a refinement of the number of spanning trees of the graph and is closely connected with the graph Laplacian matrix. In this paper, the structure of the sandpile group on the graph K3 × Cn is determined and it is shown that the Smith normal form of the sandpile group of K3 × Cn is always the direct sum of four or five cyclic groups. Our methods can be generated to the graphs K4 × Cn and K5 × Cn. © 2007 Elsevier Inc. All rights reserved.

KW - Critical group

KW - Cycle

KW - Graph Laplacian

KW - Sandpile group

KW - The Smith normal form

UR - https://www.scopus.com/pages/publications/39549104718

UR - https://www.scopus.com/record/pubmetrics.uri?eid=2-s2.0-39549104718&origin=recordpage

U2 - 10.1016/j.laa.2007.10.033

DO - 10.1016/j.laa.2007.10.033

M3 - RGC 21 - Publication in refereed journal

SN - 0024-3795

VL - 428

SP - 1886

EP - 1898

JO - Linear Algebra and Its Applications

JF - Linear Algebra and Its Applications

IS - 8-9

ER -