On Deep‐Commuting Graph of Groups

ABSTRACT The deep‐commuting graph of a finite group is the graph with vertex set such that two vertices and are adjacent if their inverse images in every central extension of commute. In this paper, we determine the structure of the deep‐commuting graph of the direct product of groups with respect to the graphs of the given groups. Also, we see that nonisomorphic finite groups may have isomorphic deep‐commuting graphs, however, finite abelian groups with isomorphic deep‐commuting graphs are isomorphic.