turkmath.org

Let G be a finite group. We define the character degree set of G, cd(G), to be the set of all character degrees of G, that is, {χ(1) : χ ∈ Irr(G)}, where Irr(G) is the set of all complex irreducible characters of G. While studying the character degree set of a finite group G, it is useful to attach some graph structure on cd(G). In this talk, we introduce some strongly related undirected graphs associated with cd(G) and present some interesting results that reflect the strong interplay between the combinatorial properties of these graphs and the structure of G.