Department of Mathematics
Graphs whose critical groups have larger rank
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. © 2011 Springer-Verlag Berlin Heidelberg.
Critical group of a graph, Laplacian matrix, Smith normal form
Source Publication Title
Acta Mathematica Sinica
Hou, Yao Ping, Wai Chee Shiu, and Wai Hong Chan. "Graphs whose critical groups have larger rank." Acta Mathematica Sinica 27.9 (2011): 1663-1670.