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
ABCDEF

Exactly one vertex of the graph has degree 1. Click it.

deg = 1
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
2.Easy

A tree has 34 edges. How many vertices |V| does it have?

|E| = 34
|V| =
3.Medium

A connected graph has 16 vertices and 23 edges. How many edges k must be removed to leave a spanning tree?

|V| = 16|E| = 23
k =
4.Medium

A connected graph has 18 vertices and 22 edges. How many edges k must be removed to leave a spanning tree?

|V| = 18|E| = 22
k =
5.Hard
ABCDE

How many walks of length 3 go from B to E? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =
6.Hard
67548121313ABCDEF

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. A
  2. 2. |V| = 35
  3. 3. k = 8
  4. 4. k = 5
  5. 5. N = 1
  6. 6. d(F) = 23

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