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
AABBCCDDEEFF010000101110010000010011010100000100

The adjacency matrix of a simple undirected graph is shown. How many edges |E| does the graph have?

|E| =
2.Easy

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

K6
|E| =
3.Medium

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

3 × deg 33 × deg 2
L =
4.Medium

A connected graph has 15 vertices and 16 edges. How many edges k must be removed to leave a spanning tree?

|V| = 15|E| = 16
k =
5.Hard
ABCDE

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

M = adjacency matrixL = 3
N =
6.Hard
8911814131710715ABCDEFG

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

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

Answer key

  1. 1. |E| = 6
  2. 2. |E| = 15
  3. 3. L = 5
  4. 4. k = 2
  5. 5. N = 1
  6. 6. W = 58

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