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

|E| = 20
|V| =
2.Easy

A forest (a graph without cycles) has 12 vertices and 2 connected components. How many edges |E| does it have?

|V| = 12c = 2
|E| =
3.Medium

A connected graph has 16 vertices and 21 edges. How many edges k must be removed to leave a spanning tree?

|V| = 16|E| = 21
k =
4.Medium

How many different Hamilton circuits H does the complete graph K7 have? Circuits that differ only in the starting vertex or the direction count as the same.

K7
H =
5.Hard
141641018212ABCDE

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

|V| = 5|E| = 7
W =
6.Hard
31614211171379ABCDEFG

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 4; skipped edges do not count.

k = 4
  1. 1edge AC
  2. 2edge BC
  3. 3edge CE
  4. 4edge DE
  5. 5edge DF
  6. 6edge GB
  7. 7edge GC
  8. 8edge GD
  9. 9edge GE

Answer key

  1. 1. |V| = 21
  2. 2. |E| = 10
  3. 3. k = 6
  4. 4. H = 360
  5. 5. W = 30
  6. 6. edge DF

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