Jabbath / Cop-Number

Checks whether the cop number of a NetworkX graph is greater than k.

k-FIXED COP NUMBER

This is a python implementation of the algorithm described in The Game of Cops and Robbers on Graphs by Anthony Bonato to solve k-FIXED COP NUMBER. The time complexity of the algorithm is O(n^{3k + 3}). This implementation is very slow for k greater than about 5 for even moderately sized graphs with 30 - 40 vertices. Currently, input graphs are treated as reflexive. If they are not reflexive, then self edges are added.

Usage

First, install the code from pip or the git repo:

pip install cop-number

Then, use a graph and a k with the copk function of cop. The function will return True if the cop number is greater than k, and False otherwise. See the example below.

import networkx as nx
from cop_number.cop import copk

G = nx.petersen_graph()

result1 = copk(G, 1)
#True

result2 = copk(G, 2)
#True

result3 = copk(G, 3)
#False

A function that automates the finding of cop number through copk has also been implemented. It can be used as follows:

import networkx as nx
from cop_number.cop import cop_num

G = nx.petersen_graph()

result = cop_num(G)
#3

Contributing

If you feel that you have something useful to add, feel free to submit a pull request.

License

Licensed under the MIT license. See license.txt.