Group exerciseChapter 4 sections 1 and 2

Determine whether the graph is connected.

SolutionFig. 1Not connected

All vertices are even.

Fig. 2Connected All vertices are even.

Try to give an example of each graph that is described. If, after several tries, you cannot find the graph that we have requested, explain why you think that it may be impossible to find that example. The degree of a vertex is the number of edges that are joined to that vertex.

1. A graph with four even vertices. 2. A graph with four odd vertices. 3. A graph with three odd vertices. 4. A graph with four vertices of degree two and two vertices of degree three.

1. Four vertices without any edges. 2.

3. Impossible 4.

Solution

If the given graph is Eulerian, find an Euler circuit. Write your answer as a sequence of vertices

A B

Duplicate edges: BD, ED

FABCD BDAED EF

How many hamilton circuits are there in K7?

Draw a K6.

1. 6! = 720

2.

Solution

Using the 3 methods to find the Hamiltonian

circuit.List the circuit and the

total weight.Start at vertex A.

AB =13; AF = 2; AD = 9; AE = 15; AC = 12BF = 10; BE = 14; BD = 7; BC = 4CD = 16; CE = 6; CF = 3DE = 8; DF = 11EF = 5

D

A

B

C

D

E

F

13 2

8 16

6

5 4

9

7

10

14 3

11

15

12

6