The Topological Graph of Frontiers is in our opinion a good graph structure representing the topology of segmented images. In this paper we deal with topological operators which achieve directly on the graph current operations performed on segmented images. Well known graph structures such as the Region Adjacency Graph [Pav77] [Ros74] do not (and cannot) keep track of the topology and so cannot maintain it. We claim that the structures and operators described here, on the contrary, allow and do this maintenance. One of the most important informations in such images is the inclusion of nested regions and one of the most important operators is the union of regions. We deal essentially with these in this paper. They are described in detail herein and we show how the topological coherence is maintained. This is why we entitle them topological operators. Other operators that we have already developed are briefly described.