Chapter 2: Graphs and Networks Lesson 2: Hello Mr Euler…

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Presentation transcript:

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

Where graph theory came from…

Where graph theory came from…

Let’s learn some definitions…

Trail (or route)

Closed Trail

Path

Cycle

Order

Connected Graph

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

A wee puzzle… F D B C E A

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