Strong equality of domination parameters in graphs - Chen, Xue-Gang,; Ma, De-Xiang, (Utilitas Mathematica, 2012)
Let Q 1 and Q 2 be properties of vertex subsets of a graph, and assume that every subset of V(G) with property Q 2 also has property Q 1. Let ψ 1 (G) and ψ 2 (G), respectively, denote the minimum cardinalities of sets with properties Q 1 and Q 2, respectively. Then ψ 1 (G) iψ 2(G). If ψ 1 (G) = ψ 2 (G) and every ψ 1(G)-set is also ψ 2 (G)-set, then we say ψ 1(G) strongly equals ψ 2(G), written ψ 1(G) ≡ iψ 2(G). In this paper, we characterize the trees and cubic graphs with γ(G) ≡ γ C(G) and γ t (G) ≡ γ c(G), where γ(G), γ t(G) and γ C(G) are the domination, total domination and connected domination numbers, respectively.