# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2018: 0.741

SCImago Journal Rank (SJR) 2018: 0.763

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

## CONNECTED ODD DOMINATING SETS IN GRAPHS

 Yair Caro Department of Mathematics University of Haifa - Oranim Tivon - 36006, Israel e-mail: yairc@macam.ac.il William F. Klostermeyer Department of Computer and Information Sciences University of North Florida Jacksonville, FL 32224, USA e-mail: klostermeyer@hotmail.com Raphael Yuster Department of Mathematics University of Haifa - Oranim Tivon - 36006, Israel e-mail: raphy@research.haifa.ac.il

## 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.

Keywords: dominating set, odd dominating set.

2000 Mathematics Subject Classification: 05C35.

## References

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