DMGT

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

ODD AND RESIDUE DOMINATION NUMBERS OF A GRAPH

Yair Caro

Department of Mathematics
University of Haifa - Oranim
Tivon - 36006, Israel
e-mail: yairc@oranim.macam98.ac.il

William F. Klostermeyer

Deptartment of Computer and Information Sciences
University of North Florida
Jacksonville, FL 32224, USA
e-mail: klostermeyer@hotmail.com

John L. Goldwasser

Department of Mathematics
West Virginia University
Morgantown, WV 26506
e-mail: jgoldwas@math.wvu.edu

Abstract

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