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