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 4 vertices (every vertex has degree 2). How many edges |E| does it have?

n = 4k = 2
|E| =
2.Easy
AABBCCDD0011001011011010

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

deg(C) =
3.Medium

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

|V| = 14|E| = 14
k =
4.Medium

A connected graph has 16 vertices and 22 edges. How many edges k must be removed to leave a spanning tree?

|V| = 16|E| = 22
k =
5.Hard
13181191239ABCDEF

Use Dijkstra’s algorithm to find the length d(F) of the shortest path from A to F in the weighted graph.

start: Aend: F
d(F) =
6.Hard
171512106162ABCDE

Find the total weight W of a minimum spanning tree of the weighted graph.

|V| = 5|E| = 7
W =

Answer key

  1. 1. |E| = 4
  2. 2. deg(C) = 3
  3. 3. k = 1
  4. 4. k = 7
  5. 5. d(F) = 19
  6. 6. W = 33

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