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| = 7
Σ deg =
2.Easy

A simple graph has 5 vertices with degrees 2, 2, 2, 2, 2. How many edges |E| does it have?

deg: 2, 2, 2, 2, 2
|E| =
3.Medium

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

2 × deg 34 × deg 4
L =
4.Medium

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

3 × deg 4
L =
5.Hard
13109819121416ABCDEF

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 5; skipped edges do not count.

k = 5
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge DF
  8. 8edge EF
6.Hard
181513121593ABCDEF

Prim’s algorithm builds a minimum spanning tree starting from vertex A. Click the edge it adds as edge number 4.

start: Ak = 4
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge CE
  5. 5edge DE
  6. 6edge DF
  7. 7edge EF
  8. 8edge BE

Answer key

  1. 1. Σ deg = 18
  2. 2. |E| = 5
  3. 3. L = 12
  4. 4. L = 8
  5. 5. edge DF
  6. 6. edge BE

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