Network in Graph Theory · Form 4
Network in Graph Theory: Paper 2 Answering Guide
How Network in Graph Theory appears in Mathematics Paper 2 (Subjective), and how to lay out your working so you earn every method mark.
How it is examined
Expect to draw or complete a network from a table or description, count degrees, and sometimes total the weights along a route. Neat diagrams matter, a cramped sketch causes miscounts.
Paper 2 questions are usually well-structured and generous with method marks if your graph is clear.
Showing your working
Mathematics Paper 2 (Subjective) is worth 100 marks and gives marks for the steps, not only the answer. Write each line clearly: state the formula or rule, substitute the numbers, then simplify.
If the question carries units, carry them through to the final line.
The question
A delivery network connects five towns P, Q, R, S and T. The roads and their lengths in km are: P–Q = 6, P–R = 9, Q–R = 4, Q–S = 7, R–S = 5, R–T = 8 and S–T = 3.
(a) State the number of vertices and the number of edges. (b) Find the degree of vertex R.
(c) Find the sum of all the degrees and verify that it equals twice the number of edges. (d) A van travels the route P → Q → S → T.
Find the total distance it covers.
Mark-earning layout, line by line
- (a) Vertices are the towns: P, Q, R, S, T → number of vertices = 5. List the roads: PQ, PR, QR, QS, RS, RT, ST → number of edges = 7.
- (b) Degree of R = number of edges meeting R. Edges at R: PR, QR, RS, RT → degree of R = 4.
- (c) Degrees: P = 2 (PQ, PR), Q = 3 (PQ, QR, QS), R = 4, S = 3 (QS, RS, ST), T = 2 (RT, ST).
- (c) Sum of degrees = 2 + 3 + 4 + 3 + 2 = 14. Twice the edges = 2 × 7 = 14. Since 14 = 14, the handshake relation is verified.
- (d) Route P → Q → S → T uses edges PQ, QS, ST. Total distance = 6 + 7 + 3 = 16 km.
Source:SPM: Format Pentaksiran mulai 2021, Matematik (1449)
Frequently asked questions
Do I get marks for listing the edges even if my final count is wrong?
Usually yes. Paper 2 awards method marks for the working, so naming every edge and showing how each degree is built earns credit even when one number slips.
A bare final answer with no working earns little if it is wrong, so always lay the steps out clearly.
Should I redraw the network the question already gives me?
If the given diagram is cramped or the question only gives a table, yes, a large, spaced redraw prevents miscounts and costs only seconds. If the printed diagram is already clear, you may annotate it directly.
Either way, mark degrees and edges on the picture you actually count from.
The route repeats a town, do I add that edge twice?
Add each edge as many times as the route actually travels it. If a route goes P → Q → P, it uses edge PQ twice, so its weight counts twice.
Follow the arrows or the listed order exactly and total the edges in the order you cross them, not the towns you pass.