1. Warm Up – 3/17 - Monday 1. 2. A) List the set of vertices.B C F G
A) List the set of vertices.
B) List the set of edges.
3. Draw a graph with V = {A, B, C}
And E = {AB, BC, AB}.

2. Definitions
A path is a sequence of edges we travel to get from one vertice to another.
A Eulerian path is a path that uses every edge exactly once.
A Eulerian circuit is a Eulerian path that starts and ends on the same vertex.

3. New Definition You can think of the degree as the
Number of lines leaving a vertex.
deg 𝐴 =3
deg 𝐵 =2
deg 𝐶 =3
deg 𝐷 =2 A B C D

4. This is a graph
Give the set of vertices and give the edge set.

5. Empty Set A set without edges can exist. 𝑉= 𝐴, 𝐵, 𝐶, 𝐷 𝐸= 𝑜𝑟 ∅
𝐸= 𝑜𝑟 ∅
∅ means “empty set”
We say the set of edges is empty because there are none.

6. Picture Not Included
On your own, draw a sketch of the graph listed above.

8. Graph Intro Classwork

9. Euler Path, Euler Circuit, or neither
#1 is an Euler Path
because I can trace all
of the edges without
repeating an edge.
It is not a Circuit because
we did not end on the
vertex we started on.

10. Definitions Each vertex is labeled with its degree or its valence
number.
Notice our circular edge
Is counted twice. We are
Counting the number of
Edges that leave a vertex.