Python NetworkX – Tutte Graph

It is a graph with 46 vertices and 69 edges. It is important because it is an exception to Tait’s conjecture which states that every 3-regular polyhedron has a Hamiltonian cycle. 

Tutte Graph

Properties of Tutte Graph:

• It is a cubic polyhedral graph which is evident from the diagram above as it is both cubic and polyhedral
• It is a Non-Hamiltonian graph.
• It is a Planar Graph.
• The chromatic number of the Tutte graph is 3.
• It can be constructed by connecting the 3 Tutte fragments such that the resulting graph is s 3-connected and planar.
• A Diagram of the Tutte fragment is given below.

Tutte Fragment

• It is evident from the above diagram that a Tutte fragment has 18 nodes.

We will use the networkx module for realizing a Tutte graph. It comes with an inbuilt function networkx.tutte_graph() and can be illustrated using the networkx.draw() method.

Syntax:

networkx.draw(G, node_size, node_color)

Parameters:

• G: It refers to the Tutte graph object
• node_size: It refers to the size of nodes.
• node_color: It refers to color of the nodes.

Below are some examples which depict how to illustrate a Tutte graph in Python:

Example 1:

Python3

# import required module
import networkx

# create object
G = networkx.tutte_graph()

# illustrate graph
networkx.draw(G)

Output:

Example 2:

Python3

# import required module
import networkx

# create object
G = networkx.tutte_graph()

# illustrate graph
networkx.draw(G, node_color='green')

Output:

Example 3:

Python3

# import required module
import networkx

# create object
G = networkx.tutte_graph()

# illustrate graph
networkx.draw(G, node_size=15,
              node_color='green')

Output:

Note: The shape of output graph illustration is generated randomly but the number, size and color of nodes will be according to the argument passed in networkx.draw() method.