powerdominationtoolbox 1.1

A package for research into power domination and variations

PowerDominationToolbox

CoCalc/Sage Integration

To maintain compatability with SageMath and the Minimum Rank Sage Library, the following commands will load this library:

URL = 'https://raw.githubusercontent.com/JibJibFlutterhousen/PowerDominationToolbox/main/PowerDominationToolbox.py'
load(URL)

For importing this library from witin CoCalc with a free account you must do the following because CoCalc does not allow an outside internet connection with a free account.

1. Download this code as a zip file.
2. Extract the zip file on your local machine.
3. Go to your project in CoCalc and upload the file "PowerDominationToolbox.py".
4. Execute the following command in your sage worksheet.

load("PowerDominationToolbox.py")

Using the Power Domination Toolbox

The PDT offers functions for:

1. Zero forcing, ZeroForce,
2. Domination, Dominate,
3. Power domination, PowerDominate,
4. Determining if a set is a power dominating set, isPDS,
5. Locating a minimum power dominating set, minpds,
6. Calculating the power domination number of a graph, pdn, and
7. Locating all minimum power dominating sets, allminpds.

Datasets

The provided graph datasets are encoded in graph6 format. For information on this graph format, please see http://users.cecs.anu.edu.au/~bdm/data/formats.txt. Dataset_1.g6 contains 600, connected, Erdos-Renyi random graphs (100 each on 20, 40, 60, 80, 100, and 120 vertices) with edge probability of 0.05. Dataset_2.g6 contains 665, connected, Erdos-Renyi random graphs on 80 vertices with edge probability of 0.05.

Funding

This project was sponsored, in part, by the Air Force Research Laboratory via the Autonomy Technology Research Center and Wright State University. This research was also supported by Air Force Office of Scientific Research award 23RYCOR004, and is Distribution A under the reference number APRS-RYA-2023-05-00002.