Abstract
A set S of vertices in a graph G is a total dominating set of G if every vertex of G is adjacent to some vertex in S. The total domination number γt(G) is the minimum cardinality of a total dominating set of G. A vertex that is contained in some minimum total dominating set of a graph G is a good vertex, otherwise it is a bad vertex. We determine for which triples (x, y, z) there exists a connected graph G with γt(G) = x and with y good vertices and z bad vertices, and we give graphs realizing these triples.
| Original language | English |
|---|---|
| Pages (from-to) | 305-315 |
| Number of pages | 11 |
| Journal | Australasian Journal of Combinatorics |
| Volume | 26 |
| Publication status | Published - 2002 |
| Externally published | Yes |
ASJC Scopus subject areas
- Discrete Mathematics and Combinatorics