Product throttling for power domination

TL;DR

This paper introduces the concept of product power throttling number in graphs, establishing bounds, characterizing extreme cases, and identifying families where it equals or differs from the domination number.

Contribution

It defines the product power throttling number for graphs and compares it to the domination number, providing bounds, characterizations, and identifying specific graph families.

Findings

Equality of parameters for paths, cycles, complete graphs, and certain grid graphs

Existence of graph families where product power throttling is less than domination number

Bounds and characterizations for graphs with extreme product power throttling numbers

Abstract

The product power throttling number of a graph is defined to study product throttling for power domination. The domination number of a graph is an upper bound for its product power throttling number. It is established that the two parameters are equal for certain families including paths, cycles, complete graphs, unit interval graphs, and grid graphs (on the plane, cylinder, and torus). Families of graphs for which the product power throttling number is less than the domination number are also exhibited. Graphs with extremely high or low product power throttling number are characterized and bounds on the product power throttling number are established.