How to generate trees with 11 and 12 vertices (with diagrams)?

Question

I looked at this thread, but I couldn't seem to understand how to use geng and nauty to generate trees and get the diagrams. I need to generate trees with 11 and 12 vertices and possibly with more vertices, and I would need the diagrams because I need to mark the color of each node.

Does anyone know a software where I can generate trees with n vertices (where n > 10) with a diagram? If diagrams are not possible, does anyone have a suggestion as to how I could efficiently mark each node in the tree without a diagram? This is part of my independent study. Thank you in advance.

Answer 1

One option is to use python, specifically networkx's generate and draw functions. As an example, to draw all (non-isomorphic) trees on 6 vertices, you can do:

import networkx as nx
import matplotlib.pyplot as plt
t = list(nx.nonisomorphic_trees(6))
fig, axs = plt.subplots(1, 6)
[nx.draw(t[i], ax=axs[i]) for i in range(6)]
plt.show()

This gives the following (quite crude!) image:

Which is maybe not the nicest tree layout, but at least shows what we want. Of course, according to A000055 there are 235 trees on 11 vertices so I assume you want them in separate images - this is certainly possible with NetworkX - and colouring the vertices can also be done.