Output list
Journal article
Classifying Character Degree Graphs with Seven Vertices
Published 01/12/2025
ADVANCES IN GROUP THEORY AND APPLICATIONS, 22, 79 - 121
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.
Journal article
On the metric dimension of the character degree graph of a solvable group
Published 11/2025
Communications in algebra, 1 - 11
Journal article
A family of graphs that cannot occur as character degree graphs of solvable groups
Published 01/09/2025
Beiträge zur Algebra und Geometrie, 66, 3, 727 - 738
We investigate character degree graphs of solvable groups. In particular, we provide general results that can be used to eliminate which degree graphs can occur for solvable groups. Finally, we show a specific family of graphs cannot occur as a character degree graph for any solvable group.
Journal article
Classifying character degree graphs with six vertices
Published 01/09/2019
Beiträge zur Algebra und Geometrie, 60, 3, 499 - 511
We investigate prime character degree graphs of solvable groups that have six vertices. There are 112 non-isomorphic connected graphs with six vertices, of which all except nine are classified in this paper. We also completely classify the disconnected graphs with six vertices.