Power domination in the generalized Petersen graphs | Zendy

Liying Kang | Zendy; Erfang Shan | Zendy; Min Zhao | Zendy

AI Assistant Blog Pricing

Home ZAIA Blog

Open Access

Power domination in the generalized Petersen graphs

Author(s) -

Liying Kang,

Erfang Shan,

Min Zhao

Publication year - 2018

Publication title -

discussiones mathematicae graph theory

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.476

H-Index - 19

eISSN - 2083-5892

pISSN - 1234-3099

DOI - 10.7151/dmgt.2137

Subject(s) - mathematics , combinatorics , domination analysis , power (physics) , discrete mathematics , graph , vertex (graph theory) , physics , quantum mechanics

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).

The content you want is available to Zendy users.

Already have an account? Click here to sign in.

Having issues? You can contact us here

Accelerating Research