Strong equality of domination parameters in trees

We study the concept of strong equality of domination parameters. Let P-1 and P-2 be properties of vertex subsets of a graph, and assume that every subset of V(G) with property P2 also has property P-1. Let psi(1)(G) and psi(2)(G), respectively, denote the minimum cardinalities of sets with properties P-1 and P-2, respectively. Then psi(1)(G) less than or equal to psi(2)(G). If psi(1)(G) = psi(2)(G) and every psi(1)(G)-set is also psi(2)(G)-set, then we say psi(1)(G) strongly equals psi(2)(G), written psi(1)(G) equivalent to psi(2)(G). We provide a constructive characterization of the trees T such that gamma(T) equivalent to i(T), where y(T) and i(T) are the domination and independent domination numbers, respectively. A constructive characterization of the trees T for which y(T) = y(t)(T), where y(t)(T) denotes the total domination number of T, is also presented. (C) 2002 Elsevier Science B.V, All fights reserved.