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 simple graph has 6 vertices with degrees 3, 3, 3, 2, 2, 1. How many edges |E| does it have?

deg: 3, 3, 3, 2, 2, 1
|E| =
2.Easy

A simple graph has 7 vertices with degrees 4, 4, 4, 4, 3, 2, 1. How many edges |E| does it have?

deg: 4, 4, 4, 4, 3, 2, 1
|E| =
3.Medium

A connected graph has 14 vertices and 17 edges. How many edges k must be removed to leave a spanning tree?

|V| = 14|E| = 17
k =
4.Medium

How many different Hamilton circuits H does the complete graph K7 have? Circuits that differ only in the starting vertex or the direction count as the same.

K7
H =
5.Hard
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Use Dijkstra’s algorithm to find the length d(E) of the shortest path from A to E in the weighted graph.

start: Aend: E
d(E) =
6.Hard
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Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 6|E| = 9
W =

Answer key

  1. 1. |E| = 7
  2. 2. |E| = 11
  3. 3. k = 4
  4. 4. H = 360
  5. 5. d(E) = 12
  6. 6. W = 38

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