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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1.Easy

How many edges |E| does the complete bipartite graph K5,10 have?

K5,10
|E| =
2.Easy
AABBCCDD0111101011001000

The adjacency matrix of a simple undirected graph is shown. How many edges |E| does the graph have?

|E| =
3.Medium

A connected graph has 13 vertices and 15 edges. How many edges k must be removed to leave a spanning tree?

|V| = 13|E| = 15
k =
4.Medium

How many different Hamilton circuits H does the complete graph K4 have? Circuits that differ only in the starting vertex or the direction count as the same.

K4
H =
5.Hard
181112311871ABCDEFG

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
8911258388ABCDEF

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

start: Aend: D
d(D) =

Answer key

  1. 1. |E| = 50
  2. 2. |E| = 4
  3. 3. k = 3
  4. 4. H = 3
  5. 5. d(F) = 23
  6. 6. d(D) = 20

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