Name
Abstract | ||
|---|---|---|
The critical ideals of a graph are the determinantal ideals of the generalized Laplacian matrix associated to a graph. A basic property of the critical ideals of graphs asserts that the graphs with at most k trivial critical ideals, @C"@?"k, are closed under induced subgraphs. In this article we find the set of minimal forbidden subgraphs for @C"@?"2, and we use this forbidden subgraphs to get a classification of the graphs in @C"@?"2. As a consequence we give a classification of the simple graphs whose critical group has two invariant factors equal to one. At the end of this article we give two infinite families of forbidden subgraphs. |
Year | DOI | Venue |
|---|---|---|
2014 | 10.1016/j.dam.2013.11.002 | Discrete Applied Mathematics |
Keywords | DocType | Volume |
critical ideal,simple graph,induced subgraphs,basic property,critical group,determinantal ideal,infinite family,generalized laplacian matrix,invariant factor,k trivial critical ideal | Journal | 167 |
ISSN | Citations | PageRank |
Discrete Applied Mathematics 167 (2014) 33-44 | 2 | 0.46 |
References | Authors | |
5 | 2 | |
Name | Order | Citations | PageRank |
|---|---|---|---|
| Carlos A. Alfaro | 1 | 7 | 2.63 |
| Carlos E. Valencia | 2 | 11 | 4.99 |