Rotation systems of some topological graph operations

In topological graph theory, rotation systems are used to capture combinatorial information of graphs that are embedded in surfaces, surface graphs. In this article, we investigate the rotation systems of some topological graph operations. Operations on surface graphs play a significant role in building classes of surface graphs. Specifically, it is possible to construct all graphs of a certain class of graphs by sequences of such operations conducting on certain graphs in the class of graphs. We examine contracted faces of degrees two, three and four in terms of rotation systems.