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 22 edges. How many vertices |V| does it have?

|E| = 22
|V| =
2.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
3.Medium

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

3 × deg 34 × deg 52 × deg 2
L =
4.Medium

A tree has 2 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?

2 × deg 44 × deg 2
L =
5.Hard
ABCDEF

How many walks of length 2 go from D to F? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 2
N =
6.Hard
10201719113ABCDE

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 3; skipped edges do not count.

k = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE

Answer key

  1. 1. |V| = 23
  2. 2. C
  3. 3. L = 17
  4. 4. L = 6
  5. 5. N = 1
  6. 6. edge CE

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