H-forming Sets in Graphs
Document Type
Article
Publication Date
2-6-2003
Description
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.
Citation Information
Haynes, Teresa W.; Hedetniemi, Stephen T.; Henning, Michael A.; and Slater, Peter J.. 2003. H-forming Sets in Graphs. Discrete Mathematics. Vol.262(1-3). 159-169. https://doi.org/10.1016/S0012-365X(02)00496-X ISSN: 0012-365X