Title

Disjoint dominating sets with a perfect matching

Document Type

Article

Publication Date

10-1-2017

Subject Area

ARRAY(0x55b843856de8)

Abstract

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.

Publication Title

Discrete Mathematics, Algorithms and Applications

Volume

9

Issue

5

Digital Object Identifier (DOI)

10.1142/S1793830917500653

ISSN

17938309

E-ISSN

17938317

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