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.

**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.

- 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 objectnode_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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