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

How many edges |E| does the complete graph K6 have?

K6
|E| =
2.Easy

A simple graph has 6 vertices with degrees 4, 2, 2, 2, 2, 2. How many edges |E| does it have?

deg: 4, 2, 2, 2, 2, 2
|E| =
3.Medium

A connected graph has 7 vertices and 17 edges. How many edges k must be removed to leave a spanning tree?

|V| = 7|E| = 17
k =
4.Medium

A connected graph has 14 vertices and 21 edges. How many edges k must be removed to leave a spanning tree?

|V| = 14|E| = 21
k =
5.Hard
ABCDE

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

M = adjacency matrixL = 2
N =
6.Hard
18151157619981ABCDEFG

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

|V| = 7|E| = 10
W =

Answer key

  1. 1. |E| = 15
  2. 2. |E| = 7
  3. 3. k = 11
  4. 4. k = 8
  5. 5. N = 1
  6. 6. W = 45

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