In this tutorial we shall learn about Hamiltonian graph.

## Definition:

A graph that contains Hamiltonian circuit is called as Hamiltonian graph.

## What is Hamiltonian circuit?

A path that passes through every vertex exactly once is called as Hamiltonian circuit. It should return to the original starting vertex.

Example:

Now we have to find if we have a Hamiltonian circuit?

If we traverse a -> b -> c -> d -> e -> a

We have a Hamiltonian path. Hence the graph is a Hamiltonian graph.

This is a NP complete problem. There is no polynomial solution.

## Hamiltonian Path:

If there is a path that starting from a vertex and visits all the vertices, but cannot return to the initial vertex. This is called as Hamiltonian path.

Example:

If we follow the path a -> b -> c -> d -> e. Here we visited all the vertices only once, but cannot return to the initial vertex. This is called as Hamiltonian path.

### Further Reading:

## Rajat

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