Slide task 6
Download as PPTX, PDF6 likes1,368 views
This document defines and provides examples of Euler paths, Euler circuits, Hamilton paths, and Hamilton circuits. An Euler path uses every edge in a graph once but starts and ends at different vertices, while an Euler circuit both uses every edge once and starts and ends at the same vertex. Similarly, a Hamilton path visits each vertex once but starts and ends at different vertices, whereas a Hamilton circuit visits each vertex once and starts and ends at the same vertex. Step-by-step processes are provided for determining if an Euler or Hamilton path or circuit exists in a graph.
Slide task 6
- 2. WHAT DO YOU UNDERSTAND ABOUT : Euler Path Euler Circuit
- 3. DEFINITION EULER PATH is a path that uses every edge of a graph exactly once.
- 5. DEFINITION EULER CIRCUIT is a circuit that uses every edge of a graph exactly once.
- 7. DIFFERENCES BETWEEN EULER PATH AND EULER CIRCUIT Euler Path-starts and ends at different vertices. Euler circuit- when a Euler path begins and ends at the same vertex
- 8. STEP BY STEP TO DETERMINE EULER PATH AND EULER CIRCUIT There are two odd vertices, A and F. Let's start at F.
- 9. Start walking at F. When you use an edge, delete it.
- 14. Path so far: FEACB
- 15. Path so far: FEACBD.
- 17. Path so far: FEACBDC
- 18. Path so far: FEACBDC Now we have to cross the bridge CF.
- 23. WHAT DO YOU UNDERSTAND ABOUT: Hamilton Path Hamilton Circuit
- 24. DEFINITION AND EXAMPLE OF HAMILTON PATH Definition: a directed path that goes through each vertex exactly once
- 25. DEFINITION AND EXAMPLE OF HAMILTON CIRCUIT is a circuit (a path that ends where it starts) that visits each vertex once without touching any vertex more than once. There may be more than one Hamilton path for a graph
- 26. DIFFERENCES BETWEEN HAMILTON PATH AND HAMILTON CIRCUIT Hamilton Path A path must have beginning and ending. Hamilton Circuit Does not have beginning / start & end is same.
- 27. STEP BY STEP TO DETERMINE HAMILTON PATH AND CIRCUIT a b cd
- 28. a b cd e