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 2-regular graph has 9 vertices (every vertex has degree 2). How many edges |E| does it have?

n = 9k = 2
|E| =
2.Easy
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The adjacency matrix of a simple undirected graph is shown. Find the degree deg(B) of vertex B.

deg(B) =
3.Medium

A connected graph has 11 vertices and 12 edges. How many edges k must be removed to leave a spanning tree?

|V| = 11|E| = 12
k =
4.Medium

A connected graph has 13 vertices and 14 edges. How many edges k must be removed to leave a spanning tree?

|V| = 13|E| = 14
k =
5.Hard
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Prim’s algorithm builds a minimum spanning tree starting from vertex A. Click the edge it adds as edge number 3.

start: Ak = 3
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE
6.Hard
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How many walks of length 3 go from B to C? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =

Answer key

  1. 1. |E| = 9
  2. 2. deg(B) = 2
  3. 3. k = 2
  4. 4. k = 2
  5. 5. edge BE
  6. 6. N = 5

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