Classifying Character Degree Graphs With 6 Vertices

TL;DR

This paper classifies prime character degree graphs with six vertices for solvable groups, covering almost all connected graphs and all disconnected graphs, thus advancing the understanding of their structure.

Contribution

It provides a complete classification of connected and disconnected prime character degree graphs with six vertices, filling gaps in existing group theory literature.

Findings

112 non-isomorphic connected graphs identified

All but nine connected graphs classified

Complete classification of disconnected graphs achieved

Abstract

We investigate prime character degree graphs of solvable groups that have six vertices. There are one hundred twelve 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.