Power domination throttling

TL;DR

This paper investigates the power domination throttling number in graphs, analyzing its computational complexity and providing methods for its calculation and bounds, with implications for related throttling variants.

Contribution

It determines the complexity of computing the power domination throttling number and introduces tools for its estimation and bounding.

Findings

Complexity of power domination throttling is established.

Tools for computing and bounding the throttling number are provided.

Results extend to variants and other aspects of power domination.

Abstract

A power dominating set of a graph $G=(V,E)$ is a set $S\subset V$ that colors every vertex of $G$ according to the following rules: in the first timestep, every vertex in $N[S]$ becomes colored; in each subsequent timestep, every vertex which is the only non-colored neighbor of some colored vertex becomes colored. The power domination throttling number of $G$ is the minimum sum of the size of a power dominating set $S$ and the number of timesteps it takes $S$ to color the graph. In this paper, we determine the complexity of power domination throttling and give some tools for computing and bounding the power domination throttling number. Some of our results apply to very general variants of throttling and to other aspects of power domination.