The College of Science in the Department of Mathematics discussed a master thesis entitled (On Hypercube Graph: Generalized k-connectivity, Domination, and Their Chromatic Polynomials) for postgraduate student Shaimaa Taleb Meerza. The thesis presented two applications related to the hypercube graph Q_n, for which we also found specific polynomials. It found the smallest local generalized connectivity of a subset S of the graph Q_n with the generalized k-connectivity κ_k (Q_n ) is the maximum number of edge-disjoint S-trees connecting S.