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 3. Click it.

deg = 3
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
2.Easy
AABBCCDDEE0110010111110010100001100

The adjacency matrix of a simple undirected graph is shown. How many edges |E| does the graph have?

|E| =
3.Medium

A connected graph has 19 vertices and 22 edges. How many edges k must be removed to leave a spanning tree?

|V| = 19|E| = 22
k =
4.Medium

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

3 × deg 33 × deg 4
L =
5.Hard
131167113103ABCDEF

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 5; A itself is round 1.

start: Around 5
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
6.Hard
ABCDE

How many walks of length 2 go from B to D? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =

Answer key

  1. 1. E
  2. 2. |E| = 6
  3. 3. k = 4
  4. 4. L = 11
  5. 5. D
  6. 6. N = 1

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