Graph Theory Review
1. Which graphs are connected?
2. Write an adjacency matrix for the following graph.
3. Find a path from start to end so that you cross every vertex exactly once.
Start
End
1 2
4. Draw a directed graph from the following adjacency matrix: [0 1
2 0
1
2]
1
5. How can you make the following graph simple? Not connected?
1 2 1
6. How many walks of length 3 go from vertex 3 to vertex 1? [0 1 2]
2 0 1
7. Which vertices are adjacent to A? Where are the parallel edges?
8. What is the degree of the graph in number 7?
9. Find the minimum weight spanning tree for the following graph.
10. Determine if the following graph has a planar representation (also know the 3 common ones that do not have
a planar representation).
11. Find the chromatic number for the graph in #10.
12. Find three numbers so that 𝑥 ≡ 2𝑚𝑜𝑑5
13. Write 111111012 in base 10.
14. A graph has an Euler circuit if __________________________________________________________
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