## DFS Exercise

Consider the following graph:

Exercise Write the vertices of the above graph in the order in which they would be visited in a depth-first traversal starting at node $0$. Assume neighbors are visited in numerical order.

## Solution

Stack | Edges | Explored |
---|---|---|

0 | - | 0 |

1 | (0, 1) | 1 |

2, 1 | (0, 2) | 2 |

5, 2, 1 | (0, 5) | 5 |

7, 2, 1 | (5, 7) | 7 |

4, 2, 1 | (7, 4) | 4 |

3, 2, 1 | (4, 3) | 3 |

6, 3, 2, 1 | (4, 6) | 6 |

8, 3, 2, 1 | (6, 8) | 8 |

3, 2, 1 | - | - |

2, 1 | - | - |

1 | - | - |

- | - | - |

The answer is $0, 1, 2, 5, 7, 4, 3, 6, 8$.