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 33 edges. How many vertices |V| does it have?

|E| = 33
|V| =
2.Easy
AABBCCDD0111101011011010

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

deg(B) =
3.Medium
ABCDEEuler circuitEuler path, no circuitneither

Does the connected graph have an Euler circuit, an Euler path that is not a circuit, or neither? Click your answer.

|V| = 5|E| = 6
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 20 vertices and 22 edges. How many edges k must be removed to leave a spanning tree?

|V| = 20|E| = 22
k =
5.Hard
6511985866ABCDEF

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
337413812104ABCDEFG

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. |V| = 34
  2. 2. deg(B) = 2
  3. 3. Euler path, no circuit
  4. 4. k = 3
  5. 5. D
  6. 6. d(F) = 18

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