Abstract
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. Copyright © 2011 Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg.
Original language | English |
---|---|
Pages (from-to) | 1663-1670 |
Journal | Acta Mathematica Sinica, English Series |
Volume | 27 |
Issue number | 9 |
DOIs | |
Publication status | Published - Sep 2011 |
Citation
Hou, Y. P., Shiu, W. C., & Chan, W. H. (2011). Graphs whose critical groups have larger rank. Acta Mathematica Sinica, English Series, 27(9), 1663-1670. doi: 10.1007/s10114-011-9358-6Keywords
- Critical group of a graph
- Laplacian matrix
- Smith normal form