Classifying Families of Character Degree Graphs of Solvable Groups
Mark W. Bissler, Jacob Laubacher

TL;DR
This paper characterizes which graphs formed by connecting two complete graphs can be realized as prime character degree graphs of solvable groups, advancing understanding of their structure.
Contribution
It provides a complete classification of the family of graphs _{k,t} as prime character degree graphs of solvable groups, identifying exactly which ones occur.
Findings
Identifies the conditions under which _{k,t} graphs occur as prime character degree graphs.
Provides a complete classification of these graphs for solvable groups.
Enhances understanding of the structure of prime character degree graphs.
Abstract
We investigate prime character degree graphs of solvable groups. In particular, we consider a family of graphs constructed by adjoining edges between two complete graphs in a one-to-one fashion. In this paper we determine completely which graphs occur as the prime character degree graph of a solvable group.
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Taxonomy
TopicsFinite Group Theory Research · graph theory and CDMA systems · Coding theory and cryptography
