Dominating sets for split and bipartite graphs
Information Processing Letters
A semi-induced subgraph characterization of upper domination perfect graphs
Journal of Graph Theory
Hereditary Domination in Graphs: Characterization with Forbidden Induced Subgraphs
SIAM Journal on Discrete Mathematics
Bounds on the connected domination number of a graph
Discrete Applied Mathematics
| Hi-index | 0.04 |
In this note, we give a finite forbidden subgraph characterization of the connected graphs for which any non-trivial connected induced subgraph has the property that the connected domination number is at most the total domination number. This question is motivated by the fact that any connected dominating set of size at least 2 is in particular a total dominating set. It turns out that in this characterization, the total domination number can equivalently be substituted by the upper total domination number, the paired-domination number and the upper paired-domination number, respectively. Another equivalent condition is given in terms of structural domination.