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ArticleOriginal scientific text

Title

Odd and residue domination numbers of a graph

Authors 1, 2, 3

Affiliations

  1. Department of Mathematics, University of Haifa - Oranim, Tivon - 36006, Israel
  2. Deptartment of Computer and Information Sciences, University of North Florida, Jacksonville, FL 32224, USA
  3. Department of Mathematics, West Virginia University, Morgantown, WV 26506

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

ENG
dominating set, odd dominating set, parity domination

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Discussiones Mathematicae Graph Theory
2001/21/1
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Pages:
119-136
Main language of publication
English
Received
2000-10-30
Accepted
2001-01-17
Published
2001

DOI: 10.7151/dmgt.1137

Exact and natural sciences