# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

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# Discussiones Mathematicae Graph Theory

## 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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