Sage code for creating an interactive element for determining chromatic number of famous graphs.

Graph coloring interact.py

from sage.graphs.graph_coloring import *
@interact
def _(graph=['Cycle Graph', 'Wheel Graph', 'Complete Graph', 'Cube Graph', 'Random'],
      n = selector([1..10], nrows = 1), p = selector([10,20,..,100], nrows = 1)):
    print graph
    if graph == 'Wheel Graph':
        print "n = %s (number of vertices)"%n
        G = graphs.WheelGraph(n)
    elif graph == 'Cycle Graph':
        print "n = %s (number of vertices)"%n
        G = graphs.CycleGraph(n)
    elif graph == 'Complete Graph':
        print "n = %s (number of vertices)"%n
        G = graphs.CompleteGraph(n)
    elif graph == 'Cube Graph':
        if n > 8:
            print "n reduced to 8"
            n = 8
        print "n = %s (dimension)"%n
        G = graphs.CubeGraph(n)
    elif graph == 'Random':
        print "n = %s (number of vertices)"%n
        print "p = %s%% (edge probability)"%p
        G = graphs.RandomGNP(n, p/100.0)
    print "Chromatic number = " + str(G.chromatic_number())
    colors = vertex_coloring(G)
    G.show(partition=colors)