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
ABCDEF

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

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

How many edges |E| does the complete graph K10 have?

K10
|E| =
3.Medium

A connected graph has 17 vertices and 25 edges. How many edges k must be removed to leave a spanning tree?

|V| = 17|E| = 25
k =
4.Medium

A tree has 2 vertices of degree 3, 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 2
L =
5.Hard
71028121195ABCDEF

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) =
6.Hard
171861037161913ABCDEF

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

|V| = 6|E| = 9
W =

Answer key

  1. 1. E
  2. 2. |E| = 45
  3. 3. k = 9
  4. 4. L = 4
  5. 5. d(E) = 12
  6. 6. W = 49

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