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 6 vertices. How many edges |E| does it have?

|V| = 6
|E| =
2.Easy

A forest (a graph without cycles) has 9 vertices and 2 connected components. How many edges |E| does it have?

|V| = 9c = 2
|E| =
3.Medium

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

3 × deg 44 × deg 2
L =
4.Medium

A connected graph has 16 vertices and 16 edges. How many edges k must be removed to leave a spanning tree?

|V| = 16|E| = 16
k =
5.Hard
1912031514114176ABCDEFG

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

|V| = 7|E| = 10
W =
6.Hard
81111259625ABCDEFG

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

start: Aend: G
d(G) =

Answer key

  1. 1. |E| = 5
  2. 2. |E| = 7
  3. 3. L = 8
  4. 4. k = 1
  5. 5. W = 56
  6. 6. d(G) = 10

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