An odd dominating set of a simple, undirected graph 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.
A variation of the problem in which one asks for the existence of a connected odd dominating set was introduced and studied in REF .
Connected odd dominating sets in graphs
Discussiones Mathematicae Graph Theory
Discussiones Mathematicae Graph Theory
Computer Science Mathematics