ON GENERALIZED MINIMAL DOMINATION PARAMETERS FOR PATHS

A subset X of vertices of a graph is a k-minimal P-set if X has property P, but the removal of any l vertices from X, where l less-than-or-equal-to k, followed by the addition of any (l - 1) vertices destroys the property P. We note that 1-minimality is the usual minimality concept. In this paper we determine-GAMMA-k(P(n)), the largest cardinality of a k-minimal dominating set of the n-vertex path P(n). We also prove for any n-vertex graph G, GAMMA-2(G)gamma(GBAR) less-than-or-equal-to n and finally a 'Gallai-type' theorem for k-minimal parameters is established.