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ArticleOriginal scientific text

Title

Connected odd dominating sets in graphs

Authors 1, 2, 1

Affiliations

  1. Department of Mathematics, University of Haifa - Oranim, Tivon - 36006, Israel
  2. Department of Computer and Information Sciences, University of North Florida, Jacksonville, FL 32224, USA

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

ENG
dominating set, odd dominating set

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Discussiones Mathematicae Graph Theory
2005/25/3
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Pages:
225-239
Main language of publication
English
Received
2003-05-07
Accepted
2005-01-19
Published
2005

DOI: 10.7151/dmgt.1276

Exact and natural sciences