Densest k-Subgraph is the problem to find a vertex subset S of size k such that number edges in subgraph induced by maximized. In this paper, we show fixed parameter tractable when parameterized neighborhood diversity, block deletion number, distance-hereditary and cograph respectively. Furthermore, give 2-approximation \(2^{{{\texttt{tc}}(G)}/2}n^{O(1)}\)-time algorithm where \({{\texttt{tc}}(...

A graph G is 1-homogeneous if certain isomorphisms between similarly embedded induced subgraphs of G extend to automorphisms of G. We show that the only connected composite 1-homogeneous graphs are the cube, and Kn ×K2 and Kn ×Kn with n ≥ 2.