Graphs whose critical groups have larger rank

Yao Ping Hou, Wai Chee SHIU, Wai Hong Chan

Research output: Contribution to journalJournal articlepeer-review

7 Citations (Scopus)


The critical group C(G) of a graph G is a refinement of the number of spanning trees of the graph and is closely connected with the Laplacian matrix. Let r(G) be the minimum number of generators (i.e., the rank) of the group C(G) and β(G) be the number of independent cycles of G. In this paper, some forbidden induced subgraphs are given for r(G) = n - 3 and all graphs with r(G) = β(G) = n - 3 are characterized.

Original languageEnglish
Pages (from-to)1663-1670
Number of pages8
JournalActa Mathematica Sinica, English Series
Issue number9
Publication statusPublished - Sept 2011

Scopus Subject Areas

  • Mathematics(all)
  • Applied Mathematics

User-Defined Keywords

  • Critical group of a graph
  • Laplacian matrix
  • Smith normal form


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