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}.

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.

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

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

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.

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

Graph Intro Classwork

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.

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.