Document Type
Article
Date of Original Version
2021
Department
Mathematics
Abstract
We give a characterization of the graphs with at most three trivial characteristic ideals. This implies the complete characterization of the regular graphs whose critical groups have at most three invariant factors equal to 1 and the characterization of the graphs whose Smith groups have at most 3 invariant factors equal to 1. We also give an alternative and simpler way to obtain the characterization of the graphs whose Smith groups have at most 3 invariant factors equal to 1, and a list of minimal forbidden graphs for the family of graphs with Smith group having at most 4 invariant factors equal to 1.
Publication Title, e.g., Journal
Linear Algebra and its Applications
Volume
615
Citation/Publisher Attribution
Alfaro, C. A., Barrus, M. D., Sinkovic, J., & Villagrán, R. R. (2021). Graphs with few trivial characteristic ideals. Linear Algebra and its Applications, 615, 155-174. https://doi.org/10.1016/j.laa.2020.12.024
Available at: https://doi.org/10.1016/j.laa.2020.12.024
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