DP Mathematics HL Questionbank

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• 12M.3dm.hl.TZ0.4b: A simple graph G has v vertices and e edges. The complement \(G'\) of G has \({e'}\) edges. (i)...
• 12M.3dm.hl.TZ0.3a: Draw the graph G .
• 12M.3dm.hl.TZ0.4a: Draw the complement of the following graph as a planar graph.
• 08M.3dm.hl.TZ1.4a: Draw G in a planar form.
• 08M.3dm.hl.TZ1.4b: Giving a reason, determine the maximum number of edges that could be added to G while keeping the...
• 08M.3dm.hl.TZ1.4c: List all the distinct Hamiltonian cycles in G beginning and ending at A, noting that two cycles...
• 08M.3dm.hl.TZ2.4b: Prove that a graph containing a triangle cannot be bipartite.
• 08M.3dm.hl.TZ2.4c: Prove that the number of edges in a bipartite graph with n vertices is less than or equal to...
• 08N.3dm.hl.TZ0.4: (a)     A connected planar graph G has e edges and v vertices. (i)     Prove that...
• 09N.3dm.hl.TZ0.5: Show that a graph is bipartite if and only if it contains only cycles of even length.
• 09N.3dm.hl.TZ0.3a: The planar graph G and its complement \(G'\) are both simple and connected. Given that G has 6...
• 10M.3dm.hl.TZ0.4: (a)     Show that, for a connected planar graph, \[v + f - e = 2.\] (b)     Assuming that...
• 11N.3dm.hl.TZ0.1a: The vertices of a graph L are A, B, C, D, E, F, G and H. The weights of the edges in L are given...
• 15N.3dm.hl.TZ0.4a: Show that \(G\) is bipartite.
• 15N.3dm.hl.TZ0.4b: State which two vertices should be joined to make \(G\) equivalent to \({K_{3,{\text{ }}3}}\).
• 15N.3dm.hl.TZ0.4d: \(H\) is a simple connected planar bipartite graph with \(e\) edges, \(f\) faces, \(v\) vertices...
• 15M.3dm.hl.TZ0.1a: The weights of the edges of a graph \(H\) are given in the following table. (i)     Draw the...
• 15M.3dm.hl.TZ0.2a: Draw \({K_{2,{\text{ }}2}}\) as a planar graph.
• 15M.3dm.hl.TZ0.4c: Draw an example of a simple connected planar graph on \(6\) vertices each of degree \(3\).
• 15M.3dm.hl.TZ0.2b: Draw a spanning tree for \({K_{2,{\text{ }}2}}\).
• 15M.3dm.hl.TZ0.2d: Show that the complement of any complete bipartite graph does not possess a spanning tree.
• 14N.3dm.hl.TZ0.2a: Use the pigeon-hole principle to prove that for any simple graph that has two or more vertices...
• 14N.3dm.hl.TZ0.2b: Seventeen people attend a meeting. Each person shakes hands with at least one other person and...