Problem Bank - Graph Theory

Access custom-built, exam-style problems for graph theory. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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Problem Bank - Graph Theory

Access custom-built, exam-style problems for graph theory. Each problem has a full solution and mark-scheme, as well as AI grading and support.

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IB: 4

0 / 6

A small autonomous delivery robot moves along raised walkways that connect five college campus buildings depicted below:

Whenever the robot reaches a building it chooses one of the outgoing walkways at random and travels to the next building.

Write down the adjacency matrix, M, for this graph.
[3]
How many different ways can the robot start at a vertex, walk exactly 5 walkways, and return to the same vertex?
[3]

0 / 9

State whether the above graph is complete.
[2]
Determine whether Kn - the complete graph of degree n - is Eulerian for
1. n=2;
  [1]
2. n=3;
  [2]
3. n=4.
  [1]
State all n for which Kn is Eulerian.
[3]

0 / 5

Find the number of edges in a complete graph on 10 vertices.
[2]

A graph is called planar if it can be drawn such that no two edges cross. All planar graphs satisfy e≤3v−6, where e is the number of edges and v is the number of vertices.