On the power domination number of the generalized Petersen graphs
- 146 Downloads
The problem of monitoring an electric power system by placing as few measurement devices in the system as possible is closely related to the well-known domination problem in graphs. Following a set of rules for power system monitoring, a set S of vertices is defined to be a power dominating set of a graph if every vertex and every edge in the system is monitored by the set S. The minimum cardinality of a power dominating set of G is the power domination number γ p (G). In this paper, we investigate the power domination number for the generalized Petersen graphs, presenting both upper bounds for such graphs and exact results for a subfamily of generalized Petersen graphs.
KeywordsPower domination number The generalized Petersen graph
Unable to display preview. Download preview PDF.
- Guo J, Niedermeier R, Raible D (2005) Improved algorithms and complexity results for power domination in graphs. In: Lecture notes comput sci, vol 3623. Springer, Berlin, pp 172–184 Google Scholar
- Fox J, Gera R, Stănică P (2007) The independence number for the generalized Petersen graphs. ARS Combin (accepted) Google Scholar
- Liao CS, Lee DT (2005) Power domination problem in graphs. In: Lecture notes comput sci, vol 3595. Springer, Berlin, pp 818–828 Google Scholar
- Mili L, Baldwin T, Phadke A (1991) Phasor measurement placement for voltage and stability monitoring and control. In: Proceeding of the EPRI-NSF workshop on application of advanced mathematics to power systems. San Franciso, CA Google Scholar