Key points are not available for this paper at this time.
The power graph of a group G is a graph with vertex set G, in which two vertices are adjacent if one is some power of the other. In the commuting graph, with G as the vertex set, two vertices are joined by an edge if they commute in G. The enhanced power graph of a group G is a graph with vertex set G and an edge joining two vertices x and y if x, y is cyclic. In this paper, we answer a question posed by P. J. Cameron, namely, if there exist groups G and H such that the power graph of G is isomorphic to the commuting graph of H. We show that the answer is yes if G is the generalised quaternion group and H is the dihedral group. We also show that the enhanced power graph of the dicyclic group is isomorphic to the commuting graph of the dihedral group.
Surbhi et al. (Sun,) studied this question.