On the sandpile group of the graph K3 × Cn

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review

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Detail(s)

Original languageEnglish
Pages (from-to)1886-1898
Journal / PublicationLinear Algebra and Its Applications
Volume428
Issue number8-9
Publication statusPublished - 15 Apr 2008

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DOI

DOI
Check@CityULib
Link to Scopus https://www.scopus.com/record/display.uri?eid=2-s2.0-39549104718&origin=recordpage
Permanent Link https://scholars.cityu.edu.hk/en/publications/publication(4d12a9f0-2dcd-4131-a0b5-43996d2859c9).html

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. © 2007 Elsevier Inc. All rights reserved.

Research Area(s)

  • Critical group, Cycle, Graph Laplacian, Sandpile group, The Smith normal form

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Publication fingerprints text

100
Sandpiles Mathematics
51
Graph in graph theo... Mathematics
28
Smith normal form Mathematics
26
Graph Laplacian Mathematics
23
Laplacian matrix Mathematics
20
Cyclic group Mathematics
19
Spanning tree Mathematics
19
Direct sum Mathematics
15
Refinement Mathematics
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Citation Format(s)

[ RIS ] [ BibTeX ]
On the sandpile group of the graph K3 × Cn. / Hou, Yaoping; Lei, Tiangang; Woo, Chingwah.
In: Linear Algebra and Its Applications, Vol. 428, No. 8-9, 15.04.2008, p. 1886-1898.

Research output: Journal Publications and Reviews (RGC: 21, 22, 62) › 21_Publication in refereed journal › peer-review