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Let G be a graph. A path factor of a graph G is a family of distinct paths with at least two vertices which forms a partition for the vertices of G. For a family of non-isomorphic graphs, F; an F-packing of G is a subgraph of G such that each of its component is isomorphic to a member of F. An F-packing P of G is called an F-factor if the set of vertices in graph G and P are the same. The F-packing problem is the problem of finding an F-packing having the maximum number of vertices in G. In graph theory packing of the vertices of paths, cycles and stars are interesting subjects . This thesis is devoted to determine the conditions under which graph G has a {Pk}-factor, where by Pk we mean a...