2019/06/01 by Benjamin M. Case, Case, Benjamin M., Todd Fenstermacher +5
Computer Science · #05C69 #Advanced Graph Theory Research #Combinatorics (math.CO) #FOS: Mathematics #Graph Labeling and Dimension Problems
paper · pdf · doi:10.48550/arxiv.1906.00135
openalex publication_date 2019/06/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A set S⊆ V is a dominating set of G if every vertex in V - S is adjacent to at least one vertex in S. The domination number γ(G) of G equals the minimum cardinality of a dominating set S in G; we say that such a set S is a γ-set. A generalization of this is partial domination which was introduced in 2017 by Case, Hedetniemi, Laskar, and Lipman [3,2] . In partial domination a set S is a p-dominating set if it dominates a proportion p of the vertices in V. The p-domination number γp(G) is the minimum cardinality of a p-dominating set in G. In this paper, we investigate further properties of partial dominating sets, particularly ones related to graph products and locating partial dominating sets. We also introduce the concept of a p-influencing set as the union of all p-dominating sets for a fixed p and investigate some of its properties.