Downhill Domination in Graphs
Document Type
Article
Publication Date
1-1-2014
Description
A path π = (v1, v2, ⋯ , vk+1) in a graph G = (V,E) is a downhill path if for every i, 1 ≤ i ≤ k, deg(vi) ≥ deg(vi+1), where deg(vi) denotes the degree of vertex vi ∈ V. The downhill domination number equals the minimum cardinality of a set S ⊆ V having the property that every vertex v ∈ V lies on a downhill path originating from some vertex in S. We investigate downhill domination numbers of graphs and give upper bounds. In particular, we show that the downhill domination number of a graph is at most half its order, and that the downhill domination number of a tree is at most one third its order. We characterize the graphs obtaining each of these bounds.
Citation Information
Haynes, Teresa W.; Hedetniemi, Stephen T.; Jamieson, Jessie D.; and Jamieson, William B.. 2014. Downhill Domination in Graphs. Discussiones Mathematicae - Graph Theory. Vol.34(3). 603-612. https://doi.org/10.7151/dmgt.1760 ISSN: 1234-3099