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

How many edges |E| does the complete bipartite graph K4,4 have?

K4,4
|E| =
2.Easy
ABCDEF

Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 6
Σ deg =
3.Medium

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

2 × deg 44 × deg 2
L =
4.Medium

A tree has 3 vertices of degree 3, 3 vertices of degree 4, 3 vertices of degree 5, 2 vertices of degree 2, and all its other vertices are leaves (degree 1). How many leaves L does it have?

3 × deg 33 × deg 43 × deg 52 × deg 2
L =
5.Hard
158131121310311ABCDEFG

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
1061422453710ABCDEFG

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) =

Answer key

  1. 1. |E| = 16
  2. 2. Σ deg = 18
  3. 3. L = 6
  4. 4. L = 20
  5. 5. d(F) = 30
  6. 6. d(E) = 12

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