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 5 vertices with degrees 3, 3, 2, 1, 1. How many edges |E| does it have?

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

A 5-regular graph has 12 vertices (every vertex has degree 5). How many edges |E| does it have?

n = 12k = 5
|E| =
3.Medium

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

2 × deg 33 × deg 43 × deg 5
L =
4.Medium

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

2 × deg 34 × deg 54 × deg 2
L =
5.Hard
5138121691719211ABCDEFG

Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 7|E| = 11
W =
6.Hard
7124941159ABCDEF

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. |E| = 5
  2. 2. |E| = 30
  3. 3. L = 19
  4. 4. L = 16
  5. 5. W = 34
  6. 6. d(F) = 17

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