On generalised 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 ≤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 Гk(Pn), the largest cardinality of a k-minimal dominating set of the n-vertex path Pn. We also prove for any n-vertex graph G, Г2(G)γ(G) ≤n and finally a 'Gallai-type' theorem for k-minimal parameters is established. © 1991, Elsevier Inc. All rights reserved.

Publication Title

Annals of Discrete Mathematics