The independent set, IS, on a graph is such that no two vertices in have an edge between them. The MIS problem on G seeks to identify an IS with maximum cardinality, i.e. MIS. is a vertex cover, i.e. VC of if every is incident upon at least one vertex in . is dominating set, DS, of if either or and . The MVC problem on G seeks to identify a vertex cover with minimum cardinality, i.e. MVC. Likewise, MCV seeks a connected vertex cover, i.e. VC which forms one component in G, with minimum cardinality, i.e. MCV. A connected DS, CDS, is a DS that forms a connected component in G. The problems MDS and MCD seek to identify a DS and a connected DS i.e. CDS respectively with minimum cardinalities. MIS, MVC, MDS, MCV and MCD on a general graph are known to be NP-complete. Polynomial time algorithms are known for bipartite graphs, chordal graphs, cycle graphs, comparability graphs, claw-free graphs, interval graphs and circular arc graphs for some of these problems. We introduce a novel graph class, layered graph, where each layer refers to a subgraph containing at most some k vertices. Inter layer edges are restricted to the vertices in adjacent layers. We show that if then MIS, MVC and MDS can be computed in polynomial time and if , where , then MCV and MCD can be computed in polynomial time. If , for , then MIS, MVC and MDS require quasi-polynomial time. If then MCV, MCD require quasi-polynomial time. Layered graphs do have constraints such as bipartiteness, planarity and acyclicity.