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-adjacen...
