Generalized connected domination in graphs
As a generalization of connected domination in a graph G we consider domination by sets having at most k components. The order gamma(k)(c) (G) of such a smallest set we relate to gamma(c)(G), the order of a smallest connected dominating set. For a tree T we give bounds on gamma(k)(c) (T) in terms of minimum valency and diameter. For trees the inequality gamma(k)(c) (T) <= n - k - 1 is known to hold, we determine the class of trees, for which equality holds.
connected domination domination tree