The diversity of domination

For any graph G and a set ~ of graphs, two distinct vertices of G are said to be ~-adjacent if they are contained in a subgraph of G which is isomorphic to a member of ~. A set S of vertices of G is an ~-dominating set (total ~¢~-dominating set) of G if every vertex in V(G)-S (V(G), respectively) is 9¢g-adjacent to a vertex in S. An ~-dominating set of G in which no two vertices are oCf-adjacent in G is an ~,~-independent dominating set of G. The minimum cardinality of an ~-dominating set, total ~-dominating set and ~-independent dominating set of G is known as the ~-domination number, total ~-domination number, and ~Yf-independent dominating number, of G, denoted, respectively, by 7ae(G),7~(G), and i~e(G). We survey the applications and bounds obtained for the above domination parameters if ~={K,} or Jf = {Pil2 ~< i ~< n}, for an integer n >/2.