Let G be a graph with a known triangular embedding in a surface S, and consider G(m), the composition of G with an independant set of order m. The purpose of this paper is to construct a triangular embedding of G(m) into a surface by using a covering triangulation with folds. We make the construction for three cases. One of them is used for proving that G(m) can be triangularly embedded into a surface if G is an Eulerian graph which can be triangularly embedded into a surface S with the same orientability characteristic as .
