The College of Science in the Department of Mathematics held a seminar entitled "Domination Number and Edge Deletion Problem of Generalized Petersen Graph" for postgraduate student Zahtaa J. Alwan. The seminar to study the Generalized Petersen Graph GP(n,k) which is a graph who's the vertex -set is V={u1,u2,…,un,v1,v2,…,v(n )} and the edge-set is E={(ui,u(i+1) ), (ui,vi ),(vi,v(i+k) );1≤i≤n} with mod n, this graph used to study the network, image processing, encryp, and others. This graph was studied from two sides: the first is domination number in the binary and triple types, and the second is the study of the effect of deleting some edges from this graph on the diameter, by attempting to solve the edge deletion problem due to the importance of this diameter as it is the best measure of network efficiency, including some results along with their proofs.