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.
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.
| Original language | English |
|---|---|
| Pages (from-to) | 225–239 |
| Journal | Discussiones Mathematicae - Graph Theory |
| Volume | 25 |
| State | Published - 2005 |