Section 5.3 GRAPH CONCEPTS AND TERMINOLOGY

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 vertexa) a loop counts twiceb) odd vertex - a vertex of odd degreec) 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

A

B

CD

E

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

A

B

CD

E

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