discrete maths
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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. A. A. C. C. B. B. E. D. D. Eulerian Graph. - PowerPoint PPT PresentationTRANSCRIPT
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
• 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