For computing the exact packing number of 3 token graph of path graph
This file is for generating the $P_n$ , $F_3(P_n)$ and $F_3^2(P_n)$ graphs automatically and then store them both in .gml and .html files
Once you have your libraries correctly installed, you just have to run the python file.
When you run it, the program will ask which
Then, once you run it, the program will generate the
When the program is finished running, you should see
You can open any html file with any web browser and you should see that graph on your window, you are free to move each node with your cursor in a dynamic way
This file is for calculating the exact value for the packing number of the $F_3(P_n)$ graph (e.g., the independence number of the $F_3^2(P_n)$ graph) and visualize the corresponding vertices of that packing set
The .nb file works with the .gml files generated in the previous step, so you should change the first and fourth lines of the file so that it is your own PC's path to the F3square.gml and F3.gml files, respectively, that you want to calculate the exact packing number for
Once you are done with these two steps, you are ready to run the Wolfram Mathematica file, for that, hit the "Evaluation" button on the program's tab and then hit the "Evaluate notebook" button as shown
Then, once it's completed running, it will show the maximum packing set vertices ID's on the second line of output, as shown, (in the case of P5, as shown, the packing number is 3, so three vertices ID's are shown)
Finally, for a visual representation, the third and fifth output lines will show the
For computing a lower bound for the packing number of 3 token graph of path graph
This file is for generating the $P_n$ , $F_3(P_n)$ and $F_3^2(P_n)$ graphs automatically and then store them both in .gml and .html files
Once you have your libraries correctly installed, you just have to run the python file.
When you run it, the program will ask which
Then, once you run it, the program will generate the
When the program is finished running, you should see
You can open any html file with any web browser and you should see that graph on your window, you are free to move each node with your cursor in a dynamic way
This file is for calculating the GDM (Graph Distance Matrix) of the $F_3(P_n)$ graph and store it on a .csv file
The .nb file works with the .gml files generated in the previous step, so you should change the first line of the file so that it is your own PC's path to the F3.gml file that you want to calculate the GDM for
You should also change the 4th input line, that is, the name of the .csv file you want Wolfram Mathematica to generate, just change the
Once you are done with these two steps, you are ready to run the Wolfram Mathematica file, for that, hit the "Evaluation" button on the program's tab and then hit the "Evaluate notebook" button as shown
Remember to wait until every line is evaluated, that is, until the last output line shows the correct name of the .csv file you are generating
Then, you will have your GDM file ready for the
For this file to work correctly, you should change the 13th, 16th and 19th lines of the file with your own data, that is, the number of nodes of the
Then you will be ready to run the program, once it's finished, the program will tell you at which row it found the best packing number, the cardinality of it, the ID's of the nodes in it and the time taken by the program to process the whole .csv file to find the best packing set.