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
ABCDEFG

Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 7
Σ deg =
2.Easy

How many edges |E| does the complete graph K4 have?

K4
|E| =
3.Medium

A connected graph has 8 vertices and 8 edges. How many edges k must be removed to leave a spanning tree?

|V| = 8|E| = 8
k =
4.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
5.Hard
11912131089ABCDE

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

start: Ak = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE
6.Hard
31125921015ABCDEF

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

Answer key

  1. 1. Σ deg = 18
  2. 2. |E| = 6
  3. 3. k = 1
  4. 4. neither
  5. 5. edge DE
  6. 6. E

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