ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

Discussiones Mathematicae Graph Theory

IMPACT FACTOR 2018: 0.741

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Discussiones Mathematicae Graph Theory


Discussiones Mathematicae Graph Theory 21(1) (2001) 119-136
DOI: 10.7151/dmgt.1137


Yair Caro

Department of Mathematics
University of Haifa - Oranim
Tivon - 36006, Israel


William F. Klostermeyer

Deptartment of Computer and Information Sciences
University of North Florida
Jacksonville, FL 32224, USA


John L. Goldwasser

Department of Mathematics
West Virginia University
Morgantown, WV 26506



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.

2000 Mathematics Subject Classification: 05C35, 05C69, 05C85.


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Received 30 October 2000
Revised 17 January 2001