On prime character degree graphs occurring within a family of graphs

Published 26 Aug 2020 in math.GR | (2008.11587v1)

Abstract: 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.

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