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Classifying Character Degree Graphs with Seven Vertices
Journal article

Classifying Character Degree Graphs with Seven Vertices

Jacob Laubacher, Mark Medwid and Dylan Schuster
ADVANCES IN GROUP THEORY AND APPLICATIONS, Vol.22, pp.79-121
01/12/2025

Abstract

Mathematics Physical Sciences Science & Technology
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.

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