الفهرس 
IntroductionOnly 14 pages are availabe for public view
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Abstract
In this Thesis, we develop the theory of cellular folding of compact connected surfaces onto polygons. Our main interest is to know whether and how many cellular foldings of a given surface onto a given polygon do exist. We classify all the possible simplicial foldings of the sphere, the connected sum of n-tori and n-projective planes onto a polygon〖 P〗_3. For each surface we get certain relations satisfied by the number of vertices, edges and faces of the simplicial decomposition of the surface.
Furthermore, we investigated the edge even graceful labeling property of the join of two graphs. Sufficient conditions for the complete bipartite graph K_(m,n) = mK_1 + nK_1 to have an edge even graceful labeling are established. Also, we introduced an edge even graceful labeling of the join of the graph K_1 with the star graph K_(1,n) , the wheel graph W_n and the sunflower graph 〖sf〗_n for all n ∈ N. We also proved that the join of the graph K_2 with the star graph K_(1,n) , the wheel graph W_n and the cyclic graph C_n are edge even graceful graphs.
Finally, by using the definition of r - edge even graceful labeling and strong r - edge even graceful, we obtained necessary and sufficient conditions for more path related graphs and cycle-related graphs to be edge even graceful graph.