On the Diameters of Commuting Graphs of Permutational Wreath Products - Leshchenko, Yu. Yu. (Ukrains’kyi Matematychnyi Zhurnal, 2014)
Let G be a group and let Z(G) be the center of G. The commuting graph of the group G is an undirected graph Γ(G) with the vertex set G Z(G) such that two vertices x, y are adjacent if and only if xy = yx. We study the commuting graphs of permutational wreath products H G, where G is a transitive permutation group acting on X (the top group of the wreath product) and (H, Y) is an Abelian permutation group acting on Y.