journal6 ›› 2005, Vol. 26 ›› Issue (4): 84-88.

• Mathematics • Previous Articles     Next Articles

Critical Groups For Some Graphs With Large Number of Edges


  1.  (1.Shaoyang Radio Television University,Shaoyang 422000,Hunan China;2.Department of Mathematics,Hunan Normal University,Changsha 410081,Hunan China)
  • Online:2005-10-15 Published:2012-09-17

Abstract: The critical group of a connected graph is a finite abelian group whose order is the number of spanning trees in the graph and is closely related to the graph Laplacian.In this paper,the critical groups for some graphs with large number of edges,such as Kn-K1,m,Kn-Km,Kn-mK2,Kn,n-nK2,are determined completely.

Key words: graph laplacian, critical group, the Smith normal form

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