Practice IB Mathematics Applications & Interpretation (AI) Topic AHL 3.14—graph Theory with authentic exam-style questions for both SL and HL students. This question bank focuses on the exact syllabus content for AHL 3.14—graph Theory and mirrors Paper 1, 2, 3 style where relevant.
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Write down the number of friendships in the network.
Write down the maximum degree of any user in the network.
Write down the degree sequence of the network in non-increasing order.
Find a subset of users such that every pair of users in the subset are friends.
State whether the network is connected, justifying your answer.
The network would become a complete graph if all possible friendships were present. Calculate the number of additional friendships that would need to be added to the network to make it complete.
A particle moves in a plane such that its position vector (in metres) at time seconds, for , is given by .
Find the velocity vector, , of the particle in terms of .
Find the position vector of the particle at the instant its speed is at a minimum.
On a transport graph, a drone has position vector (in metres) relative to vertex at time seconds, for , given by .
Find the velocity vector, , in terms of .
Find the position vector of the drone at the instant its speed is at a minimum.
Demonstrate that the handshaking lemma holds for the graph .
Provide evidence that cannot be drawn as a planar graph.
Determine, providing a brief explanation, whether possesses an Eulerian circuit.
Write down the number of vertices of .
Write down the number of edges of .
Write down the degree of vertex .
State whether is a simple graph. Justify your answer.