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
ABCDEFG

Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 7
Σ deg =
2.Easy

How many edges |E| does the complete bipartite graph K4,11 have?

K4,11
|E| =
3.Medium

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

2 × deg 34 × deg 42 × deg 54 × deg 2
L =
4.Medium

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

4 × deg 34 × deg 44 × deg 53 × deg 2
L =
5.Hard
19126895171ABCDEF

Prim’s algorithm builds a minimum spanning tree starting from vertex E. Click the edge it adds as edge number 3.

start: Ek = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge DE
  6. 6edge DF
  7. 7edge EF
  8. 8edge BE
6.Hard
ABCDE

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

M = adjacency matrixL = 3
N =

Answer key

  1. 1. Σ deg = 16
  2. 2. |E| = 44
  3. 3. L = 18
  4. 4. L = 26
  5. 5. edge BD
  6. 6. N = 6

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