Abstract
For graphs G and H, a set S⊆V(G) is an H-forming set of G if for every v∈V(G)-S, there exists a subset R⊆S, where |R|=|V(H)|-1, such that the subgraph induced by R∪{v} contains H as a subgraph (not necessarily induced). The minimum cardinality of an H-forming set of G is the H-forming number γ {H}(G). The H-forming number of G is a generalization of the domination number γ(G) because γ(G)=γ {P2}(G) . We show that γ(G)γ {P3}(G)γ t(G), where γ t(G) is the total domination number of G. For a nontrivial tree T, we show that γ {P3}(T)=γ t(T). We also define independent P 3-forming sets, give complexity results for the independent P 3-forming problem, and characterize the trees having an independent P 3-forming set.
Original language | English |
---|---|
Pages (from-to) | 159-169 |
Number of pages | 11 |
Journal | Discrete Mathematics |
Volume | 262 |
Issue number | 1-3 |
DOIs | |
Publication status | Published - 6 Feb 2003 |
Externally published | Yes |
Keywords
- Domination
- H-forming number
- Independence
- Total domination
ASJC Scopus subject areas
- Theoretical Computer Science
- Discrete Mathematics and Combinatorics