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The Critical Group of Km × Cn 被引量：1

The Critical Group of Km × Cn
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摘要 In this paper, the structure of the critical group of the graph Km × Cn is determined, where m, n ≥3. In this paper, the structure of the critical group of the graph Km × Cn is determined, where m, n ≥3.
作者 Jian WANG Yong Liang PAN Jun Ming XU
机构地区 Department of Mathematics
出处 《Acta Mathematica Sinica,English Series》 SCIE CSCD 2011年第1期169-184,共16页 数学学报（英文版）
基金 Supported by National Natural Science Foundation of China （Grant Nos. 10871189 and 10671191） and Chinese Universities Scientific Fund
关键词 GRAPH Laplacian matrix critical group invariant factor Smith normal form tree number Graph, Laplacian matrix, critical group, invariant factor, Smith normal form, tree number
分类号 TM721.1 [电气工程—电力系统及自动化] O613.71 [理学—无机化学]
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参考文献14

  • 1Bacher, R., de la Harpe, P.: The lattices of integral flows and the lattices of integral cuts of a finite graph. Bull. Soc. Math. France, 125, 167-198 (1997).
  • 2Biggs, N. L.: Algebraic potential theory on graphs. Bull. London Math. Soc., 29, 641-682 (1997).
  • 3Biggs, N. L.: Chip-Firing and the critical group of a graph. Journal of Algebraic Combinatorics, 9, 25-45 (1999).
  • 4Godsil, C., Royle, G., Algebraic Graph Theory, GTM 207, Springer-Verlag, New York, 2001.
  • 5Cori, R., Rossin, D.: On the sandpile group of dual graphs. European J. Combin., 21, 447-459 (2000).
  • 6Cori, R., Leborgne, Y.: Sandpile model and Tutte polynomial. Adv. Appl. Math., 30, 44-52 (2003).
  • 7Dartois, A., Fiorenzi, F., Francini, P.: Sandpile group on the graph :Dn of the dihedral group. European J. Combin., 24, 815-824 (2003).
  • 8Merris, R.: Unimodular equivalence of graphs. Linear Algebra Appl., 173, 181-189 (1992).
  • 9Lorenzini, D, J.: A finite group attached to the Laplacian of a graph. Discrete Math., 91, 277-282 (1991).
  • 10Jacobson, B., Niedermaier, A., Reiner, V.: Critical groups for complete multipartite graphs and cartesian products of complete graphs. J. Graph Theory, 44, 231-250 (2003).

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Acta Mathematica Sinica,English Series
2011年 第1期

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