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

How many edges |E| does the complete graph K9 have?

K9
|E| =
2.Easy
AABBCCDD0111101011011010

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

|E| =
3.Medium
ABCDEFGEuler 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| = 7|E| = 9
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 18 vertices and 22 edges. How many edges k must be removed to leave a spanning tree?

|V| = 18|E| = 22
k =
5.Hard
15141431813799ABCDEFG

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 3; A itself is round 1.

start: Around 3
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
6.Hard
12172948201815ABCDEFG

Prim’s algorithm builds a minimum spanning tree starting from vertex E. Click the edge it adds as edge number 3.

start: Ek = 3
  1. 1edge AC
  2. 2edge BC
  3. 3edge BD
  4. 4edge CE
  5. 5edge DE
  6. 6edge DF
  7. 7edge EF
  8. 8edge GC
  9. 9edge GD

Answer key

  1. 1. |E| = 36
  2. 2. |E| = 5
  3. 3. neither
  4. 4. k = 5
  5. 5. B
  6. 6. edge DF

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