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
AABBCCDD0101101001001000

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

|E| =
2.Easy
ABCDEFG

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

|V| = 7
Σ deg =
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| = 10
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 6 vertices and 8 edges. How many edges k must be removed to leave a spanning tree?

|V| = 6|E| = 8
k =
5.Hard
9141658313ABCDE

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 AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE
6.Hard
1539181415212ABCDEFG

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

Answer key

  1. 1. |E| = 3
  2. 2. Σ deg = 20
  3. 3. neither
  4. 4. k = 3
  5. 5. edge CE
  6. 6. C

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