Year 12 Further Maths - Chapter 14 Test 1 - Networks

Five towns, A, B, C, D and E are connected by roads. A graph of these connections, where roads are represented by edges and towns are represented by vertices, is shown below. The degree of the vertex representing town B is

• 1

• 2

• 3

• 4

• 5

A woman drives along some of the roads to visit some of the towns along the following route: E – A – B – C – D – E. The walk she follows is best described as a

• walk only

• trail

• path

• circuit

• cycle

A planar graph has 7 vertices and 11 edges. The number of faces that the graph has is

• 2

• 3

• 4

• 5

• 6

Using the graph on the right, a walk that is also a hamiltonian path is

• A – E – B – C – A – E – D

• A – E – B – C – D – E

• A – E – B – C – D

• A – E – B – C – D – E – A

• A – E – B – C

The shortest route from P to W in the diagram on the right has length

• 11

• 12

• 13

• 18

• 19

For the graph shown here, the minimum spanning tree has total weight

• 11

• 13

• 15

• 18

• 24

The graph on the right would have an eulerian trail if an edge was added between vertices

• A and D

• B and F

• B and D

• E and B

• E and F

Consider the graph on the right. Which one of the following statements is not true?

• A circuit and cycle are both impossible to walk.

• The graph does not have a hamiltonian cycle.

• The graph has an eulerian trail but not an eulerian circuit.

• The sum of the degrees of the vertices is 14.

• The graph has a hamiltonian path.

Which one of the graphs below cannot be redrawn in planar form?

• 
• 
• 
• 
• 

Five towns, A, B, C, D and E are connected by roads. A graph of these connections, where roads are represented by edges and towns are represented by vertices, is shown below. This graph has

• one odd degree vertex and five even degree vertices

• two odd degree vertices and four even degree vertices

• three odd degree vertices and three even degree vertices

• four odd degree vertices and two even degree vertices

• five odd degree vertices and one even degree vertices