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 simple graph has 5 vertices with degrees 3, 3, 2, 2, 2. How many edges |E| does it have?

deg: 3, 3, 2, 2, 2
|E| =
2.Easy

A simple graph has 7 vertices with degrees 4, 4, 4, 3, 3, 2, 2. How many edges |E| does it have?

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

How many different Hamilton circuits H does the complete graph K8 have? Circuits that differ only in the starting vertex or the direction count as the same.

K8
H =
4.Medium

A connected graph has 16 vertices and 25 edges. How many edges k must be removed to leave a spanning tree?

|V| = 16|E| = 25
k =
5.Hard
1615810911ABCDE

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

start: Ck = 2
  1. 1edge AB
  2. 2edge AC
  3. 3edge BC
  4. 4edge BD
  5. 5edge CE
  6. 6edge DE
  7. 7edge BE
6.Hard
ABCDEF

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

M = adjacency matrixL = 2
N =

Answer key

  1. 1. |E| = 6
  2. 2. |E| = 11
  3. 3. H = 2520
  4. 4. k = 10
  5. 5. edge AB
  6. 6. N = 1

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