On some Graphs Related to Regular, Oriented Triangular Maps

We examine the graphψ(G, λ),where the vertices are given by the elements of the conjugacy classλof the finite groupG,and then adjacency (∼) given byv∼u⇔bothuv2andvu2are involutions andu≠v.In particular, under certain conditions on the pair (G, λ)we may derive fromψ(G, λ)a second graphξ(G, λ)which constitutes disjoint copies of underlying graphs of certain regular oriented triangular maps.