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 4-regular graph has 10 vertices (every vertex has degree 4). How many edges |E| does it have?

n = 10k = 4
|E| =
2.Easy

A tree has 34 edges. How many vertices |V| does it have?

|E| = 34
|V| =
3.Medium
ABCDEFEuler 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| = 6|E| = 6
  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
ABCDEF

How many closed walks of length 2 start and end at D? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =
6.Hard
22015137119116ABCDEFG

Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 7|E| = 9
W =

Answer key

  1. 1. |E| = 20
  2. 2. |V| = 35
  3. 3. neither
  4. 4. k = 3
  5. 5. N = 3
  6. 6. W = 46

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