Geodesic
Odd and residue domination numbers of a graph
Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 119-136

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Let G = (V,E) be a simple, undirected graph. A set of vertices D is called an odd dominating set if |N[v] ∩ D| ≡ 1 (mod 2) for every vertex v ∈ V(G). The minimum cardinality of an odd dominating set is called the odd domination number of G, denoted by γ₁(G). In this paper, several algorithmic and structural results are presented on this parameter for grids, complements of powers of cycles, and other graph classes as well as for more general forms of "residue" domination.
Keywords: dominating set, odd dominating set, parity domination 
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Caro, Yair; Klostermeyer, William; Goldwasser, John. Odd and residue domination numbers of a graph. Discussiones Mathematicae. Graph Theory, Tome 21 (2001) no. 1, pp. 119-136. http://geodesic.mathdoc.fr/item/DMGT_2001_21_1_a8/