Where Are Planar 0-Vertex Graphs Hiding?

Euler's theorem about the relationship between the numbers of individual elements of planar graphs (vertices, edges, faces) is also satisfied when the graph has zero vertices. The problem of the existence or not of such graphs has so far been the subject of very few studies. Plus, research that didn't prove anything. The paper presents an interpretation of this kind of graphs as mathematical formations lying on piecewise smooth surfaces. The lines of intersection of two or more smooth surfaces (faces of a graph) form edges without a vertex of the graph. The elementary properties of such graphs are discussed, the method of counting non-isomorphic 0-vertex graphs and their importance in physics and chemistry are given.