# Connected odd dominating sets in graphs

• Volume: 25, Issue: 3, page 225-239
• ISSN: 2083-5892

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## Abstract

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An odd dominating set of a simple, undirected graph G = (V,E) is a set of vertices D ⊆ V such that |N[v] ∩ D| ≡ 1 mod 2 for all vertices v ∈ V. It is known that every graph has an odd dominating set. In this paper we consider the concept of connected odd dominating sets. We prove that the problem of deciding if a graph has a connected odd dominating set is NP-complete. We also determine the existence or non-existence of such sets in several classes of graphs. Among other results, we prove there are only 15 grid graphs that have a connected odd dominating set.

## How to cite

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Yair Caro, William F. Klostermeyer, and Raphael Yuster. "Connected odd dominating sets in graphs." Discussiones Mathematicae Graph Theory 25.3 (2005): 225-239. <http://eudml.org/doc/270479>.

@article{YairCaro2005,
abstract = {An odd dominating set of a simple, undirected graph G = (V,E) is a set of vertices D ⊆ V such that |N[v] ∩ D| ≡ 1 mod 2 for all vertices v ∈ V. It is known that every graph has an odd dominating set. In this paper we consider the concept of connected odd dominating sets. We prove that the problem of deciding if a graph has a connected odd dominating set is NP-complete. We also determine the existence or non-existence of such sets in several classes of graphs. Among other results, we prove there are only 15 grid graphs that have a connected odd dominating set.},
author = {Yair Caro, William F. Klostermeyer, Raphael Yuster},
journal = {Discussiones Mathematicae Graph Theory},
keywords = {dominating set; odd dominating set},
language = {eng},
number = {3},
pages = {225-239},
title = {Connected odd dominating sets in graphs},
url = {http://eudml.org/doc/270479},
volume = {25},
year = {2005},
}

TY - JOUR
AU - Yair Caro
AU - William F. Klostermeyer
AU - Raphael Yuster
TI - Connected odd dominating sets in graphs
JO - Discussiones Mathematicae Graph Theory
PY - 2005
VL - 25
IS - 3
SP - 225
EP - 239
AB - An odd dominating set of a simple, undirected graph G = (V,E) is a set of vertices D ⊆ V such that |N[v] ∩ D| ≡ 1 mod 2 for all vertices v ∈ V. It is known that every graph has an odd dominating set. In this paper we consider the concept of connected odd dominating sets. We prove that the problem of deciding if a graph has a connected odd dominating set is NP-complete. We also determine the existence or non-existence of such sets in several classes of graphs. Among other results, we prove there are only 15 grid graphs that have a connected odd dominating set.
LA - eng
KW - dominating set; odd dominating set
UR - http://eudml.org/doc/270479
ER -

## References

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11. [11] J. Goldwasser, W. Klostermeyer and H. Ware, Fibonacci polynomials and parity domination in grid graphs, Graphs and Combinatorics 18 (2002) 271-283, doi: 10.1007/s003730200020. Zbl0999.05079
12. [12] M. Halldorsson, J. Kratochvil and J. Telle, Mod-2 independence and domination in graphs, in: Proceedings Workshop on Graph-Theoretic Concepts in Computer Science '99, Ascona, Switzerland (Springer-Verlag, Lecture Notes in Computer Science, 1999) 101-109. Zbl0943.05081
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