Disjoint dominating sets with a perfect matching
In this paper, we consider dominating sets D and D′ such that D and D′ are disjoint and there exists a perfect matching between them. Let DDm(G) denote the cardinality of smallest such sets D,D′ in G (provided they exist, otherwise DDm(G) = ∞). This concept was introduced in [W. F. Klostermeyer, M. E. Messinger and A. Angeli Ayello, An eternal domination problem in grids, Theory Appl. Graphs 4(1) (2017) 23pp.] in the context of studying a certain graph protection problem. We characterize the trees T for which DDm(T) equals a certain graph protection parameter and for which DDm(T) = α(T), where α(G) is the independence number of G. We also further study this parameter in graph products, e.g., by giving bounds for grid graphs, and in graphs of small independence number.
Discrete Mathematics, Algorithms and Applications
Digital Object Identifier (DOI)
Klostermeyer, Messinger, M.-E., & Ayello, A. A. (2017). Disjoint dominating sets with a perfect matching. Discrete Mathematics, Algorithms, and Applications, 9(5), 1750065–. https://doi.org/10.1142/S1793830917500653