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 simple graph has 7 vertices with degrees 4, 4, 3, 3, 3, 2, 1. How many edges |E| does it have?

deg: 4, 4, 3, 3, 3, 2, 1
|E| =
2.Easy
ABCDEF

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

|V| = 6
Σ deg =
3.Medium

A connected graph has 20 vertices and 30 edges. How many edges k must be removed to leave a spanning tree?

|V| = 20|E| = 30
k =
4.Medium

A connected graph has 8 vertices and 13 edges. How many edges k must be removed to leave a spanning tree?

|V| = 8|E| = 13
k =
5.Hard
14711617152ABCDE

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

|V| = 5|E| = 7
W =
6.Hard
2075931517ABCDE

Prim’s algorithm builds a minimum spanning tree starting from vertex C. Click the edge it adds as edge number 2.

start: Ck = 2
  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. |E| = 10
  2. 2. Σ deg = 14
  3. 3. k = 11
  4. 4. k = 6
  5. 5. W = 25
  6. 6. edge BC

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