1. Can you draw this picture without lifting up your pen/pencil?

2. How about this one?

3. Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY

4. 1) Degree of a vertex - the number of edges at the vertex a) a loop counts twice b) odd vertex - a vertex of odd degree c) even vertex - a vertex of even degree
List all of the odd vertices: __________________
List even vertices: _____________________

5. 2) Adjacent vertices - two vertices are adjacent if there is an edge joining them 3) Adjacent edges - two edges are adjacent if they share a common vertex
List a pair of adjacent vertices: __________
List a pair of adjacent edges: ___________

6. 4) Path - a sequence of vertices such that each vertex in the sequence is adjacent to the next one and no edge appears in the path more than once.
*** The number of edges in a path is called the length of the path. Each edge has a length of 1; a loop has length of 1
List a path of length 5 from A to G:
___________________
List a path of length 7 from A to G:

7. 5) Circuit - a path which starts and ends at the same vertex (multiple edges and loops are circuits).
List 2 circuits and give their length
_______________

8. 6) Connected graph - a graph for which any two of its vertices can be joined by a path 7) Disconnected graph - a graph made up of connected pieces

9. 8) Euler path - a path which travels through every edge of a graphB E C D
Example: An Euler path: D, E, A, B, E, C, B, D, C

10. 9) Euler circuit - a circuit which travels through every edge of a graph
Example: An Euler circuit:
D, E, A, B, E, C, B, D, C, F, D B D C F

11. 10) Bridge - an edge, which if removed, disconnects the graph
Is there a bridge?
If yes, which one?
_______________

12. Draw a graph with 3 vertices, each of degree 2
Draw a connected graph with 3 vertices, each of degree 4