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 tree has 37 edges. How many vertices |V| does it have?

|E| = 37
|V| =
2.Easy

How many edges |E| does the complete graph K5 have?

K5
|E| =
3.Medium

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

4 × deg 32 × deg 2
L =
4.Medium

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

4 × deg 34 × deg 2
L =
5.Hard
19169517201341ABCDEF

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

|V| = 6|E| = 9
W =
6.Hard
859191115128ABCDEFG

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. |V| = 38
  2. 2. |E| = 10
  3. 3. L = 6
  4. 4. L = 6
  5. 5. W = 35
  6. 6. d(F) = 15

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