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
AABBCCDD0111101011011010

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

deg(D) =
2.Easy
ABCDEFG

Find the sum of the degrees of all vertices of the graph shown, Σ deg.

|V| = 7
Σ deg =
3.Medium

How many different Hamilton circuits H does the complete graph K4 have? Circuits that differ only in the starting vertex or the direction count as the same.

K4
H =
4.Medium

A connected graph has 14 vertices and 24 edges. How many edges k must be removed to leave a spanning tree?

|V| = 14|E| = 24
k =
5.Hard
412151315621214ABCDEFG

Dijkstra’s algorithm runs from A. Click the vertex that is settled (made permanent) in round 4; A itself is round 1.

start: Around 4
  1. 1A
  2. 2B
  3. 3C
  4. 4D
  5. 5E
  6. 6F
  7. 7G
6.Hard
3174514720ABCDE

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

start: Ak = 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. deg(D) = 2
  2. 2. Σ deg = 18
  3. 3. H = 3
  4. 4. k = 11
  5. 5. C
  6. 6. edge DE

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