Recent Results on the Power Domination Numbers of Graph Products

Authors

  • K. W. Soh The University of Auckland
  • K. M. Koh Singapore University of Technology and Design

DOI:

https://doi.org/10.53733/36

Keywords:

Electric power monitoring, Power domination, Graph products

Abstract

We review recent results on the power domination problem of graph products and establish improved results for some families of graph products, namely, C_{n} \times C_{m}, P_{n} \times C_{m}, Pn ⊠ Pm, Pn ⊠ Cm and Cn ⊠ Cm. We also characterize graphs G and H for which the power domination number of the Cartesian product of G and H, which is denoted as \gamma_{p}(G \;\Box\;H), is 1.

 

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Author Biographies

K. W. Soh, The University of Auckland

Department of Engineering Science,

The University of Auckland,

70 Symonds Street,

Auckland 1010

K. M. Koh, Singapore University of Technology and Design

Engineering Systems and Design,

Singapore University of Technology and Design,

8 Somapah Road,

Singapore 487372

 

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Published

31-12-2018

How to Cite

Soh, K. W. ., & Koh, K. M. . (2018). Recent Results on the Power Domination Numbers of Graph Products. New Zealand Journal of Mathematics, 48, 41–53. https://doi.org/10.53733/36

Issue

Vol. 48 (2018)

Section

Articles