1 of 8 0-day streak

A full network investigation

Question 1 of 8

Calculator allowed

The network shows cycling routes between trail junctions. The graph is connected and can be drawn in planar form. Each edge label gives the cycling time in minutes

(a)3 marks

Determine the values of v, e and f. Include the infinite outer face in f

v e f

(b)1 mark

Count the vertices whose degrees are odd

Number of odd vertices

Is it possible to use each connection once and finish at the start? Select the justified verdict

Yes. The graph is connected and every vertex has even degree

No. The graph is connected with exactly two odd vertices, so only an open Eulerian trail is possible

No. Four odd vertices prevent an Eulerian trail or circuit

No. The edge set is split into disconnected components

(d)1 mark

By inspection, calculate the least possible total cycling time for a path from Orchard to Creek

Shortest-path total (minutes)

(e)1 mark

Calculate the minimum total weight of cycling-route sections that connect every location in the network

Minimum connector total (minutes)