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 moduleimport networkx# create objectG = networkx.tutte_graph() # illustrate graphnetworkx.draw(G) |
Output:
Example 2:
Python3
# import required moduleimport networkx# create objectG = networkx.tutte_graph()# illustrate graphnetworkx.draw(G, node_color='green') |
Output:
Example 3:
Python3
# import required moduleimport networkx# create objectG = networkx.tutte_graph()# illustrate graphnetworkx.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.
