Discrete Maths Chapter 2: Graphs and Networks Lesson 2: Hello Mr Euler…
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Discrete Maths Chapter 2: Graphs and Networks Lesson 2: Hello Mr Euler…
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Transcript of Discrete Maths 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…
Let’s learn some definitions…
Trail (or route)
Closed Trail
Path
Cycle
Order
Connected Graph
Eulerian Graph
• CHECK: A connected graph is Eulerian if and only if every node has an even order
√ X
• A connected graph which has a closed trail containing every arc precisely once
A
B
C
DE
A
B C
D
A wee puzzle…
F
D
B
CE
A
Semi-Eulerian Graph
• CHECK: A connected graph is Semi-Eulerian if and only if precisely two nodes have odd order
• A graph which has a trail that is not closed that contains every arc precisely once
F
D
B
CE
A
