# DMGT

ISSN 1234-3099 (print version)

ISSN 2083-5892 (electronic version)

# IMPACT FACTOR 2019: 0.755

SCImago Journal Rank (SJR) 2019: 0.600

Rejection Rate (2018-2019): c. 84%

# Discussiones Mathematicae Graph Theory

Article in press

Authors:

L. Kang, E. Shan, M. Zhao

Title:

Domination in the generalized Petersen graphs

Source:

Discussiones Mathematicae Graph Theory

Received: 2017-07-31, Revised: 2018-02-26, Accepted: 2018-02-26, https://doi.org/10.7151/dmgt.2137

Abstract:

The problem of monitoring an electric power system by placing as few measurement devices in the system can be formulated as a power dominating set problem in graph theory. The power domination number of a graph is the minimum cardinality of a power dominating set. Xu and Kang [On the power domination number of the generalized Petersen graphs, J. Comb. Optim. 22 (2011) 282–291] study the exact power domination number for the generalized Petersen graph $P(3k,k)$, and propose the following problem: determine the power domination number for the generalized Petersen graph $P(4k,k)$ or $P(ck,k)$. In this paper we give the power domination number for $P(4k,k)$ and present a sharp upper bound on the power domination number for the generalized Petersen graph $P(ck,k)$.

Keywords:

power domination, domination, generalized Petersen graph, electric power system