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Python NetworkX – Tutte Graph
• Last Updated : 29 Apr, 2021

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.

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