Network in Graph Theory · Form 4
Network in Graph Theory: Revision Notes
A tight revision summary of Network in Graph Theory for SPM Mathematics, the key ideas, the formulae the exam gives you, and what to focus on before the paper.
The big idea
A network (graph) is a set of points, called vertices, joined by lines, called edges. This chapter teaches you to read and draw networks, count degrees, find the sum of weights on the edges, and use them to model real situations like routes and connections.
Key ideas to revise
- Vertices, edges and degree. The degree of a vertex is how many edges meet at it, the most common quick question.
- Directed and weighted networks. Edges can carry a direction (one-way) or a weight (a distance or cost), read which kind the question uses.
- Drawing a network from a description. Turning a worded situation into a clear graph is the skill Paper 2 rewards most here.
One worked mini-example per key idea
- Degree at a vertex: vertex B is joined to A, C and D, plus one loop at B. The ordinary edges give 3, the loop adds 2, so degree of B = 3 + 2 = 5.
- Directed network: at vertex T, 2 arrows point in and 3 point out. In-degree = 2, out-degree = 3, so total degree = 2 + 3 = 5.
- Weighted route: a van goes P → Q → R with edge weights 7 km and 4 km. Total weight of the route = 7 + 4 = 11 km.
- Network from a table: a table lists the links A–B, A–C, B–C and C–D. That is 4 edges, and vertex C is joined to A, B and D, so degree of C = 3.
Your pre-paper checklist for this chapter
- Re-derive the handshake relation yourself: the total of all degrees = 2 × (number of edges). Use it to fill a missing degree and to catch a miscount, the total can never be odd.
- Know what the exam hands you: usually a diagram, a table of links, or a description, plus any weights or the edge count. You rarely have to invent data.
- Redraw every network large and well spaced before counting anything, cramped edges are the main cause of a wrong degree.
- Separate a loop (adds 2 to the degree) from a pair of parallel edges (each counts once) and from a directed edge (keep in-degree and out-degree apart).
- The one habit that saves marks: label every vertex and show your degree count edge by edge, then check with the handshake total before moving on.
Source:DSKP KSSM Mathematics Form 4 and 5 (Versi English)
Frequently asked questions
How should I set out my revision so degree questions become automatic?
Work on one clear, well-spaced diagram and mark each vertex's degree beside it as you count edge by edge. Then add all the degrees and check the total is twice the edge count.
Doing this on three or four small networks makes the counting habit stick under exam pressure.
Does a loop really change my revision counting?
Yes, and it is worth a whole revision slot. A loop starts and ends at the same vertex, so it meets that vertex twice and adds 2 to the degree, not 1.
Miss this and your degree total turns odd, which is impossible, a clear sign of the slip you can catch yourself.
What does the exam always provide versus what I must work out?
The paper gives you the raw picture, a diagram, a table of links, or a worded description, plus any weights or the edge count. What you supply is the reading: degrees, totals, a route's weight, or a clean redrawn graph.
Knowing the split stops you inventing data you were meant to read off.