Campus Units
Mathematics, Electrical and Computer Engineering
Document Type
Article
Publication Version
Accepted Manuscript
Publication Date
12-31-2018
Journal or Book Title
Discrete Applied Mathematics
Volume
251
First Page
103
Last Page
113
DOI
10.1016/j.dam.2018.06.004
Abstract
A power dominating set of a graph G is a set S of vertices that can observe the entire graph under the rules that (1) the closed neighborhood of every vertex in S is observed, and (2) if a vertex and all but one of its neighbors are observed, then the remaining neighbor is observed; the second rule is applied iteratively. The power domination number of G, denoted by gamma p(G), is the minimum number of vertices in a power dominating set. A Nordhaus-Gaddum problem for power domination is to determine a tight lower or upper bound on gamma p(G) + gamma p(G) or gamma p(G).gamma p(G), where G denotes the complement of G. The upper and lower Nordhaus-Gaddum bounds over all graphs for the power domination number follow from known bounds on the domination number and examples. In this note we improve the upper sum bound for the power domination number substantially for graphs having the property that both the graph and its complement are connected. For these graphs, our bound is tight and is also significantly better than the corresponding bound for the domination number. We also improve the product upper bound for the power domination number for graphs with certain properties.
Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-No Derivative Works 4.0 International License.
Copyright Owner
Elsevier B.V.
Copyright Date
2018
Language
en
File Format
application/pdf
Recommended Citation
Benson, Katherine F.; Ferrero, Daniela; Flagg, Mary; Furst, Veronika; Hogben, Leslie; and Vasilevska, Violeta, "Nordhaus–Gaddum problems for power domination" (2018). Mathematics Publications. 205.
https://lib.dr.iastate.edu/math_pubs/205
Comments
This is a manuscript of an article published as Benson, Katherine F., Daniela Ferrero, Mary Flagg, Veronika Furst, Leslie Hogben, and Violeta Vasilevska. "Nordhaus–Gaddum problems for power domination." Discrete Applied Mathematics 251 (2018): 103-113. DOI: 10.1016/j.dam.2018.06.004. Posted with permission.