On prime character degree graphs occurring within a family of graphs

Jacob Laubacher, Mark Medwid

Published 2020-08-26Version 1

In this paper we investigate families of connected graphs which do not contain an odd cycle in their complement. Specifically, we consider graphs formed by two complete graphs connected in a particular way. We determine which of these graphs can or cannot occur as the prime character degree graph of a solvable group. An obvious expansion and generalization can also be considered, of which we make mention.