Graph theory worksheet with answers

Free printable Graph theory worksheet: 6 problems from easy to exam level, with an answer key. Print it or save it as a PDF.

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Name: ____________________   Date: ____________

1.Easy
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Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 5
Σ deg =
2.Easy

How many edges |E| does the complete bipartite graph K6,4 have?

K6,4
|E| =
3.Medium

A tree has 4 vertices of degree 3, 3 vertices of degree 4, 2 vertices of degree 5, 2 vertices of degree 2, and all its other vertices are leaves (degree 1). How many leaves L does it have?

4 × deg 33 × deg 42 × deg 52 × deg 2
L =
4.Medium

A tree has 2 vertices of degree 3, 2 vertices of degree 4, 3 vertices of degree 5, and all its other vertices are leaves (degree 1). How many leaves L does it have?

2 × deg 32 × deg 43 × deg 5
L =
5.Hard
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Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 7|E| = 9
W =
6.Hard
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Prim’s algorithm builds a minimum spanning tree starting from vertex C. Click the edge it adds as edge number 3.

start: Ck = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE

Answer key

  1. 1. Σ deg = 14
  2. 2. |E| = 24
  3. 3. L = 18
  4. 4. L = 17
  5. 5. W = 43
  6. 6. edge DE

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