Strong equality of domination parameters in trees

Teresa W. Haynes, Michael A. Henning, Peter J. Slater
2003 Discrete Mathematics  
We study the concept of strong equality of domination parameters. Let P1 and P2 be properties of vertex subsets of a graph, and assume that every subset of V (G) with property P2 also has property P1. Let 1(G) and 2(G), respectively, denote the minimum cardinalities of sets with properties P1 and P2, respectively. Then 1(G) 6 2(G). If 1(G)= 2(G) and every 1(G)-set is also a 2(G)-set, then we say 1(G) strongly equals 2(G), written 1(G) ≡ 2(G). We provide a constructive characterization of the
more » ... es T such that (T ) ≡ i(T ), where (T ) and i(T ) are the domination and independent domination numbers, respectively. A constructive characterization of the trees T for which (T ) = t (T ), where t (T ) denotes the total domination number of T , is also presented.
doi:10.1016/s0012-365x(02)00451-x fatcat:bdignvioj5abrisjidnkso63zm