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 tree has 19 vertices. How many edges |E| does it have?

|V| = 19
|E| =
2.Easy
ABCDE

Exactly one vertex of the graph has degree 4. Click it.

deg = 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
3.Medium

A connected graph has 18 vertices and 25 edges. How many edges k must be removed to leave a spanning tree?

|V| = 18|E| = 25
k =
4.Medium

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

3 × deg 33 × deg 42 × deg 5
L =
5.Hard
17414512201021ABCDEF

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

|V| = 6|E| = 9
W =
6.Hard
63882310126ABCDEFG

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| = 18
  2. 2. B
  3. 3. k = 8
  4. 4. L = 17
  5. 5. W = 24
  6. 6. d(F) = 19

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