Add to ORKGA vertex that is contained in some minimum dominating set of a graph G is a good vertex, otherwise it is bad. Let g(G) (respectively, b(G)) denote the number of good (respectively, bad) vertices in a graph G. We determine for which triples (x, y, z) there exists a graph G such that γ(G) = x, g(G) = y, and b(G) = z. Then we give graphs realizing these triples. Also, we show that no graph has g(G) = b(G) = γ(G) and characterize the graphs G for which g(G) = b(G) = γ(G) + 1
AbstractLet G be a graph and γ(G) denote the domination number of G. A dominating set D of a graph G...
In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a g...
A set D of vertices of a graph G = (VG, EG) is a dominating set of G if every vertex in VG — D is ad...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
For a graph G, a set S is a dominating set if every vertex in V-S has a neighbor in S. A vertex cont...
The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every...
The γ-graph γ·G of a graph G is the graph whose vertices are labelled by the minimum dominating sets...
In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V(G) is a double dominating ...
A set S ⊆ V is a dominating set of a graph G = (V,E) if every vertex in V -S is adjacent to at least...
AbstractWe are interested in a notion of domination related to both vertices and edges of graphs. We...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a g...
Let kk be a positive integer and let GG be a graph with vertex set V(G)V(G). A subset D⊆V(G)D\subset...
A dominating set of a graph G is a set D⊆ VG such that every vertex in VG- D is adjacent to at least...
AbstractLet G be a graph and γ(G) denote the domination number of G. A dominating set D of a graph G...
In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a g...
A set D of vertices of a graph G = (VG, EG) is a dominating set of G if every vertex in VG — D is ad...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
For a graph G, a set S is a dominating set if every vertex in V-S has a neighbor in S. A vertex cont...
The domination number γ(G) of a graph G is the minimum number of vertices in a set D such that every...
The γ-graph γ·G of a graph G is the graph whose vertices are labelled by the minimum dominating sets...
In a graph G, a vertex dominates itself and its neighbors. A subset S ⊆ V(G) is a double dominating ...
A set S ⊆ V is a dominating set of a graph G = (V,E) if every vertex in V -S is adjacent to at least...
AbstractWe are interested in a notion of domination related to both vertices and edges of graphs. We...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to ...
In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a g...
Let kk be a positive integer and let GG be a graph with vertex set V(G)V(G). A subset D⊆V(G)D\subset...
A dominating set of a graph G is a set D⊆ VG such that every vertex in VG- D is adjacent to at least...
AbstractLet G be a graph and γ(G) denote the domination number of G. A dominating set D of a graph G...
In a graph a vertex is said to dominate itself and all its neighbors. A double dominating set of a g...
A set D of vertices of a graph G = (VG, EG) is a dominating set of G if every vertex in VG — D is ad...