1. Chapter 2: Graphs and Networks Lesson 2: Hello Mr Euler…
Discrete Maths
Chapter 2: Graphs and Networks
Lesson 2: Hello Mr Euler…

2. Where graph theory came from…

3. Where graph theory came from…

5. Let’s learn some definitions…

6. Trail (or route)

7. Closed Trail

8. Path

9. Cycle

10. Order

11. Connected Graph

12. Eulerian Graph
A connected graph which has a closed trail containing every arc precisely once A B C D A B C D E √ X
CHECK: A connected graph is Eulerian if and only if every node has an even order

13. A wee puzzle… F D B C E A

14. Semi-Eulerian Graph
A graph which has a trail that is not closed that contains every arc precisely once F D B C E A
CHECK: A connected graph is Semi-Eulerian if and only if precisely two nodes have odd order