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Mathematics Worksheet
🕸️ Graph Theory
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Find the degree of a vertex.Apply the handshake theorem (degree sum = 2 × edges).Recognise paths and cycles.Relate degree sum to the number of edges.🧠 Section A · Concept Check ● BEGINNER 4 × 1 = 4
1Edges A-B, B-C, C-D, D-A, A-C. The degree of vertex A is:
2Using the same graph, the degree of vertex C is:
3A graph has 6 edges. The sum of all vertex degrees is:
4If the sum of vertex degrees is 14, the number of edges is:
🧮 Section B · Problem Solving ● INTERMEDIATE 2 + 3×3 = 11
5The of a vertex is its number of incident edges.
6The sum of all degrees equals × the number of edges.
7Edges A-B, B-C, C-D, D-A, A-C. Find the degree of vertex A.
8Using the same graph, find the degree of vertex C.
9A graph has 6 edges. Find the sum of all vertex degrees.
🚀 Section C · Challenge ● CHALLENGE 5
10If the sum of vertex degrees is 14, how many edges does the graph have?
💭 Reflection — the most useful thing I learned:
A ___/4 B ___/11 C ___/5 Total ___/20
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✂ answer key — fold or cut before handing out
1-A 2-A 3-A 4-A | 5 degree 6 2 7 = 3 (B, D, C) 8 = 3 (B, D, A) 9 = 12 | 10 = 7