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
AABBCCDDEE0100010111010010100001100

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

|E| =
2.Easy

A simple graph has 6 vertices with degrees 3, 3, 3, 2, 2, 1. How many edges |E| does it have?

deg: 3, 3, 3, 2, 2, 1
|E| =
3.Medium

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

2 × deg 32 × deg 43 × deg 2
L =
4.Medium

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

2 × deg 3
L =
5.Hard
5810179162ABCDE

Kruskal’s algorithm builds a minimum spanning tree. Click the edge it adds as edge number 3; skipped edges do not count.

k = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE
6.Hard
11713197811ABCDE

Prim’s algorithm builds a minimum spanning tree starting from vertex D. Click the edge it adds as edge number 4.

start: Dk = 4
  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| = 5
  2. 2. |E| = 7
  3. 3. L = 8
  4. 4. L = 4
  5. 5. edge AC
  6. 6. edge AB

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