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 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| =
2.Easy
AABBCCDDEE0110010101110010000101110

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

deg(B) =
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| = 9
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A connected graph has 17 vertices and 21 edges. How many edges k must be removed to leave a spanning tree?

|V| = 17|E| = 21
k =
5.Hard
1914762082101ABCDEFG

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

|V| = 7|E| = 9
W =
6.Hard
8111125655ABCDEF

Use Dijkstra’s algorithm to find the length d(F) of the shortest path from A to F in the weighted graph.

start: Aend: F
d(F) =

Answer key

  1. 1. |E| = 5
  2. 2. deg(B) = 3
  3. 3. neither
  4. 4. k = 5
  5. 5. W = 51
  6. 6. d(F) = 18

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