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 2-regular graph has 7 vertices (every vertex has degree 2). How many edges |E| does it have?

n = 7k = 2
|E| =
2.Easy
AABBCCDDEEFF001000001010110000000010010101000010

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

|E| =
3.Medium

A connected graph has 13 vertices and 20 edges. How many edges k must be removed to leave a spanning tree?

|V| = 13|E| = 20
k =
4.Medium

How many different Hamilton circuits H does the complete graph K4 have? Circuits that differ only in the starting vertex or the direction count as the same.

K4
H =
5.Hard
ABCDE

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

M = adjacency matrixL = 2
N =
6.Hard
9471193110ABCDEF

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| = 7
  2. 2. |E| = 5
  3. 3. k = 8
  4. 4. H = 3
  5. 5. N = 2
  6. 6. d(F) = 19

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