Recent Results on the Power Domination Numbers of Graph Products

Soh, K. W.; Koh, K. M.

doi:10.53733/36

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Cited by 3 publications

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Power Domination in Graphs

Dorbec

2020

Topics in Domination in Graphs

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In this chapter, we are interested in power domination in graphs. Power domination is a variation of domination introduced to address a physical problem of monitoring a network with phasor measurement units. The originality of this variation is that some propagation happens, and the set of covered vertices results from an iterative process. We present a survey of known results on this specific parameter.

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Power Domination in Graphs

Dorbec

2020

Topics in Domination in Graphs

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On the power domination number of the Cartesian product of graphs

Koh

Soh

2019

AKCE International Journal of Graphs and Combinatorics

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Some product graphs with power dominating number at most 2

Shahbaznejad

Kazemi

Pelayo

2021

AKCE International Journal of Graphs and Combinatorics

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Let S be a set of vertices of a graph G. Let M½S be the set of vertices built from the closed neighborhood N½S of S, by iteratively applying the following propagation rule: if a vertex and all but exactly one of its neighbors are in M½S, then the remaining neighbor is also in M½S: A set S is called a power dominating set of G if M½S ¼ VðGÞ: The power domination number c P ðGÞ of G is the minimum cardinality of a power dominating set. In this paper, we present some necessary conditions for two graphs G and H to satisfy 1 c P ðG Ã HÞ 2 for product graphs.

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Recent Results on the Power Domination Numbers of Graph Products

Cited by 3 publications

References 9 publications

Power Domination in Graphs

Power Domination in Graphs

On the power domination number of the Cartesian product of graphs

Some product graphs with power dominating number at most 2

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