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
AABBCCDDEEFF011000101110110010010001011001000110

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

deg(A) =
2.Easy

A simple graph has 5 vertices with degrees 3, 2, 2, 2, 1. How many edges |E| does it have?

deg: 3, 2, 2, 2, 1
|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| = 8
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 8 vertices and 14 edges. How many edges k must be removed to leave a spanning tree?

|V| = 8|E| = 14
k =
5.Hard
18841411910ABCDEF

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
6.Hard
511915219318121713ABCDEFG

Prim’s algorithm builds a minimum spanning tree starting from vertex D. Click the edge it adds as edge number 5.

start: Dk = 5
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge CE
  5. 5edge DE
  6. 6edge DF
  7. 7edge EF
  8. 8edge GB
  9. 9edge GC
  10. 10edge GD
  11. 11edge GE

Answer key

  1. 1. deg(A) = 2
  2. 2. |E| = 5
  3. 3. neither
  4. 4. k = 7
  5. 5. F
  6. 6. edge BC

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