We study the concept of strong equality of domination parameters. Let P1and P2be properties of vertex subsets of a graph, and assume that every subset of V(G) with property P2also has property P1. Let ψ1(G) and ψ2(G), respectively, denote the minimum cardinalities of sets with properties P1and P2, respectively. Then ψ1(G) ≤ ψ2(G). If ψ1(G)=ψ2(G) and every ψ1(G)-set is also a ψ2(G)-set, then we say ψ1(G) strongly equals ψ2(G), written ψ1(G) = ψ2(G). We provide a constructive characterization of the trees T such that γ(T) = i(T), where γ(T) and i(T) are the domination and independent domination numbers, respectively. A constructive characterization of the trees T for which γ(T) = γt(T), where γt(T) denotes the total domination number of T, is also presented. © 2002 Elsevier Science B.V. All rights reserved.
Haynes, T. W., Henning, M. A., & Slater, P. J. (2003). Strong equality of domination parameters in trees. Discrete Mathematics, 260(1–3), 77–87. https://doi.org/10.1016/s0012-365x(02)00451-x