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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1.Easy

A simple graph has 7 vertices with degrees 4, 4, 4, 3, 3, 2, 2. How many edges |E| does it have?

deg: 4, 4, 4, 3, 3, 2, 2
|E| =
2.Easy
AABBCCDDEE0100010111010010100101110

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

|E| =
3.Medium

A tree has 4 vertices of degree 3, 3 vertices of degree 2, and all its other vertices are leaves (degree 1). How many leaves L does it have?

4 × deg 33 × deg 2
L =
4.Medium

A tree has 2 vertices of degree 3, 3 vertices of degree 4, 3 vertices of degree 5, and all its other vertices are leaves (degree 1). How many leaves L does it have?

2 × deg 33 × deg 43 × deg 5
L =
5.Hard
2712159121514ABCDEF

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) =
6.Hard
ABCDEF

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

M = adjacency matrixL = 2
N =

Answer key

  1. 1. |E| = 11
  2. 2. |E| = 6
  3. 3. L = 6
  4. 4. L = 19
  5. 5. d(F) = 29
  6. 6. N = 3

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