The structure of the character degree graphs Δ(G), i.e. the prime graphs on the set cd(G) of the irreducible character degrees of a finite group G, such that G is solvable and Δ(G) has diameter three, remains an intriguing area of study. However, a comprehensive understanding of these structures remains elusive. In this paper, we prove some properties and provide an infinite series of examples of this class of graphs, building on the ideas of M. Lewis [8].
Dolfi, S., Hafezieh, R., Spiga, P. (2026). On the structure of the character degree graphs having diameter three. JOURNAL OF ALGEBRA, 685(1 January 2026), 337-360 [10.1016/j.jalgebra.2025.08.002].
On the structure of the character degree graphs having diameter three
Spiga P.
2026
Abstract
The structure of the character degree graphs Δ(G), i.e. the prime graphs on the set cd(G) of the irreducible character degrees of a finite group G, such that G is solvable and Δ(G) has diameter three, remains an intriguing area of study. However, a comprehensive understanding of these structures remains elusive. In this paper, we prove some properties and provide an infinite series of examples of this class of graphs, building on the ideas of M. Lewis [8].
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