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

A tree has 19 vertices. How many edges |E| does it have?

|V| = 19
|E| =
2.Easy

A tree has 34 edges. How many vertices |V| does it have?

|E| = 34
|V| =
3.Medium

A connected graph has 20 vertices and 23 edges. How many edges k must be removed to leave a spanning tree?

|V| = 20|E| = 23
k =
4.Medium

A connected graph has 16 vertices and 19 edges. How many edges k must be removed to leave a spanning tree?

|V| = 16|E| = 19
k =
5.Hard
15831283132ABCDEF

Use Dijkstra’s algorithm to find the length d(F) of the shortest path from A to F in the weighted graph.

start: Aend: F
d(F) =
6.Hard
10314715481ABCDEFG

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 4; A itself is round 1.

start: Around 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G

Answer key

  1. 1. |E| = 18
  2. 2. |V| = 35
  3. 3. k = 4
  4. 4. k = 4
  5. 5. d(F) = 26
  6. 6. D

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