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
AABBCCDDEE0110010101110010000101110

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

deg(E) =
2.Easy

A tree has 9 edges. How many vertices |V| does it have?

|E| = 9
|V| =
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 tree has 4 vertices of degree 5, 2 vertices of degree 2, and all its other vertices are leaves (degree 1). How many leaves L does it have?

4 × deg 52 × deg 2
L =
5.Hard
7418212519615ABCDEFG

Prim’s algorithm builds a minimum spanning tree starting from vertex B. Click the edge it adds as edge number 4.

start: Bk = 4
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DF
  7. 7edge EF
  8. 8edge GB
  9. 9edge GC
  10. 10edge GE
6.Hard
4615813217ABCDEF

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 2; skipped edges do not count.

k = 2
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge DF
  8. 8edge EF

Answer key

  1. 1. deg(E) = 3
  2. 2. |V| = 10
  3. 3. Euler path, no circuit
  4. 4. L = 14
  5. 5. edge AB
  6. 6. edge DF

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