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
AABBCCDDEE0110010111110000100101010

The adjacency matrix of a simple undirected graph is shown. Find the degree deg(C) of vertex C.

deg(C) =
2.Easy
AABBCCDDEE0110010111110010100101110

The adjacency matrix of a simple undirected graph is shown. Find the degree deg(E) of vertex E.

deg(E) =
3.Medium
ABCDEFGEuler circuitEuler path, no circuitneither

Does the connected graph have an Euler circuit, an Euler path that is not a circuit, or neither? Click your answer.

|V| = 7|E| = 11
  1. 1Euler circuit
  2. 2Euler path, no circuit
  3. 3neither
4.Medium

A tree has 4 vertices of degree 3, 3 vertices of degree 4, 3 vertices of degree 5, and all its other vertices are leaves (degree 1). How many leaves L does it have?

4 × deg 33 × deg 43 × deg 5
L =
5.Hard
ABCDE

How many closed walks of length 3 start and end at C? A walk may repeat vertices and edges. Call the number N.

M = adjacency matrixL = 3
N =
6.Hard
65415138119ABCDEF

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

start: Dk = 2
  1. 1edge AC
  2. 2edge BC
  3. 3edge BD
  4. 4edge CE
  5. 5edge DE
  6. 6edge DF
  7. 7edge EF
  8. 8edge BE

Answer key

  1. 1. deg(C) = 2
  2. 2. deg(E) = 3
  3. 3. Euler path, no circuit
  4. 4. L = 21
  5. 5. N = 4
  6. 6. edge BC

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