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

How about this one?

Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY

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: _____________________

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: ___________

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:

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 _______________

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

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

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

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

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