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 28 edges. How many vertices |V| does it have?

|E| = 28
|V| =
2.Easy

How many edges |E| does the complete graph K10 have?

K10
|E| =
3.Medium

How many different Hamilton circuits H does the complete graph K5 have? Circuits that differ only in the starting vertex or the direction count as the same.

K5
H =
4.Medium

A connected graph has 10 vertices and 15 edges. How many edges k must be removed to leave a spanning tree?

|V| = 10|E| = 15
k =
5.Hard
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Use Dijkstra’s algorithm to find the length d(G) of the shortest path from A to G in the weighted graph.

start: Aend: G
d(G) =
6.Hard
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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) =

Answer key

  1. 1. |V| = 29
  2. 2. |E| = 45
  3. 3. H = 12
  4. 4. k = 6
  5. 5. d(G) = 15
  6. 6. d(F) = 13

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