ABSTRACT
For a set S ~ V(G) to be a dominating set of G, it is required that N[S] = V(G) or, equivalently, that for each v E V(G), N[v] n S # 0. In other words, every v E V (G) must be dominated by at least one vertex in S (possibly itself). For the tree T1 in Figure 4.1 with S = {v3, v5, vg, v13}, each of vi> Vz, v4, Vs, V7, vs, Vg, vu, Vtz, v 13, and Vt4 is dominated exactly once, while V3, v5, and v10 are dominated twice. The motivating idea for this chapter is to attempt to dominate every vertex exactly once. The focus shifts from the order of the (dominatin€i, packing, ... ) set to the amount of domination being done.
