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 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
2.Easy
AABBCCDDEE0110010100110010000100110

The adjacency matrix of a simple undirected graph is shown. Find the degree deg(D) of vertex D.

deg(D) =
3.Medium

A connected graph has 16 vertices and 21 edges. How many edges k must be removed to leave a spanning tree?

|V| = 16|E| = 21
k =
4.Medium

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

3 × deg 4
L =
5.Hard
14101281053115ABCDEFG

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 4; A itself is round 1.

start: Around 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
6.Hard
1115431114101510ABCDEF

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. deg(D) = 1
  3. 3. k = 6
  4. 4. L = 8
  5. 5. G
  6. 6. d(F) = 24

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