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
ABCDEFG

Exactly one vertex of the graph has degree 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
2.Easy

A tree has 17 vertices. How many edges |E| does it have?

|V| = 17
|E| =
3.Medium

A connected graph has 14 vertices and 21 edges. How many edges k must be removed to leave a spanning tree?

|V| = 14|E| = 21
k =
4.Medium

A tree has 4 vertices of degree 4, 4 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?

4 × deg 44 × deg 52 × deg 2
L =
5.Hard
1311035916177198ABCDEFG

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

|V| = 7|E| = 11
W =
6.Hard
14761242710ABCDEF

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. F
  2. 2. |E| = 16
  3. 3. k = 8
  4. 4. L = 22
  5. 5. W = 41
  6. 6. d(F) = 22

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