Search topics

Search
1 of 8 0-day streak

A full network investigation

DIFFICULTYstandardchallenge
QUESTION TYPEMix of allChange
Five-part investigation; all-even six-vertex networkFive-part investigation; two-odd six-vertex networkNOWMix of allRecommended
Question 1 of 8

Calculator allowed

Consider this plan of paths between campus buildings. The graph is connected and can be drawn in planar form. Each edge label gives the walking time in minutes

Weighted investigation network. Vertices in listed order: [Hall | Canteen | Science | Workshop | Arts | Library]. Full edge list: Science–Canteen (2 minutes); Canteen–Hall (10 minutes); Workshop–Hall (16 minutes); Library–Canteen (8 minutes); Arts–Hall (14 minutes); Hall–Library (22 minutes); Science–Workshop (6 minutes).2 minutes10 minutes16 minutes8 minutes14 minutes22 minutes6 minutesHallCanteenScienceWorkshopArtsLibrary
(a)3 marks

Record v and e for this graph and calculate f using v + f = e + 2

(b)1 mark

Determine the number of odd-degree vertices in the network

(c)1 mark

Decide whether an edge-exact closed traversal exists. Choose the matching reason

(d)1 mark

What is the minimum route total between Workshop and Library?

(e)1 mark

What is the least possible total walking time for campus paths reaching all vertices?