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
AABBCCDD0010001011010010

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

|E| =
2.Easy

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

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

A connected graph has 14 vertices and 16 edges. How many edges k must be removed to leave a spanning tree?

|V| = 14|E| = 16
k =
4.Medium

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

4 × deg 34 × deg 43 × deg 2
L =
5.Hard
1484133476ABCDEF

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
1089131233915ABCDEFG

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| = 3
  2. 2. |E| = 5
  3. 3. k = 3
  4. 4. L = 14
  5. 5. D
  6. 6. d(F) = 24

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