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
AABBCCDDEE0100010111010010100001100

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

|E| =
2.Easy

A simple graph has 7 vertices with degrees 4, 3, 3, 3, 1, 1, 1. How many edges |E| does it have?

deg: 4, 3, 3, 3, 1, 1, 1
|E| =
3.Medium
ABCDEEuler 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| = 5|E| = 5
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 13 vertices and 23 edges. How many edges k must be removed to leave a spanning tree?

|V| = 13|E| = 23
k =
5.Hard
75125995310ABCDEF

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
12431197217ABCDEF

Prim’s algorithm builds a minimum spanning tree starting from vertex B. Click the edge it adds as edge number 2.

start: Bk = 2
  1. 1edge AB
  2. 2edge AC
  3. 3edge BD
  4. 4edge CE
  5. 5edge DE
  6. 6edge DF
  7. 7edge EF
  8. 8edge BE

Answer key

  1. 1. |E| = 5
  2. 2. |E| = 8
  3. 3. neither
  4. 4. k = 11
  5. 5. E
  6. 6. edge DF

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