enumeration of the number of spanning trees in some ... - Toubkal

134 CHAPTER 7. MAXIMAL PLANAR MAPSIn future, we plan to work on the planar maps of type C= C 1 ‡ C 2 with ‡ is notat all a simple path, and shall try to generalize the theorem deletion - contraction byworking on deletion more than one edge, i.e., the theorem deletion - contraction workedon one edge but we shall work on n edges and associate it with our results in this thesis.Keywords graphs, maps, trees, spanning trees, complexity, Laplacian matrix, Matrix-Tree Theorem, the n-Fan chains, the n- Grid chains, star flower planar map, maximalplanar map, Wiener index.