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 6 vertices with degrees 4, 2, 2, 2, 1, 1. How many edges |E| does it have?

deg: 4, 2, 2, 2, 1, 1
|E| =
2.Easy

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

deg: 4, 4, 3, 3, 2, 2, 2
|E| =
3.Medium

A connected graph has 18 vertices and 18 edges. How many edges k must be removed to leave a spanning tree?

|V| = 18|E| = 18
k =
4.Medium

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

2 × deg 34 × deg 5
L =
5.Hard
4116121039ABCDEF

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
102113410101292ABCDEFG

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| = 6
  2. 2. |E| = 10
  3. 3. k = 1
  4. 4. L = 16
  5. 5. d(F) = 8
  6. 6. d(G) = 13

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