Classifying character degree graphs with seven vertices
Group Theory
2023-08-03 v1 Combinatorics
Abstract
We study here the graphs with seven vertices in an effort to classify which of them appear as the prime character degree graphs of finite solvable groups. This classification is complete for the disconnected graphs. Of the 853 non-isomorphic connected graphs, we were able to demonstrate that twenty-two occur as prime character degree graphs. Two are of diameter three, while the remaining are constructed as direct products. Forty-four graphs remain unclassified.
Cite
@article{arxiv.2308.01216,
title = {Classifying character degree graphs with seven vertices},
author = {Jacob Laubacher and Mark Medwid and Dylan Schuster},
journal= {arXiv preprint arXiv:2308.01216},
year = {2023}
}
Comments
28 pages, 18 figures. arXiv admin note: text overlap with arXiv:2108.08330