DP Mathematics HL Questionbank

Description

Directly related questions

• 18M.3dm.hl.TZ0.3c: Let T be a tree with \(v\) where \(v\) ≥ 2. Use the handshaking lemma to prove that T has at...
• 18M.3dm.hl.TZ0.3b.i: In the context of graph theory, state the handshaking lemma.
• 18M.3dm.hl.TZ0.3a.iii: Draw \({\kappa _{3,\,2}}\) and explain why it does not have a Hamiltonian cycle.
• 18M.3dm.hl.TZ0.3a.ii: Show that \({\kappa _{3,\,3}}\) has a Hamiltonian cycle.
• 18M.3dm.hl.TZ0.3a.i: Draw \({\kappa _{3,\,3}}\).
• 16M.3dm.hl.TZ0.5c: show that \({v^2} - 13v + 24 \leqslant 0\) and hence determine the maximum possible value of \(v\).
• 16M.3dm.hl.TZ0.5b: show that the sum of the number of faces in \(G\) and the number of faces in \(G'\) is...
• 16M.3dm.hl.TZ0.5a: Show that the number of edges in \(G'\), the complement of \(G\), is...
• 16N.3dm.hl.TZ0.2c: a tree cannot exist with a degree sequence of...
• 16N.3dm.hl.TZ0.2b: a simple, connected, planar graph cannot exist with a degree sequence of...
• 16N.3dm.hl.TZ0.2a: a graph cannot exist with a degree sequence of...
• 17N.3dm.hl.TZ0.3b: A connected graph \(G\) has \(v\) vertices. Prove, using Euler’s relation, that a spanning tree...
• 17N.3dm.hl.TZ0.3a.ii: Prove that \({\kappa _{3,3}}\) is not planar.
• 17N.3dm.hl.TZ0.3a.i: Draw the complete bipartite graph \({\kappa _{3,3}}\).
• 17N.3dm.hl.TZ0.3c: If an edge \(E\) is chosen at random from the edges of \({\kappa _n}\), show that the probability...
• 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 .
• 08M.3dm.hl.TZ1.5b: (i)     A tree has v vertices. State the number of edges in the tree, justifying your...
• SPNone.3dm.hl.TZ0.2b: Giving a reason, state whether or not G is (i)     simple; (ii)     connected; (iii)    ...
• SPNone.3dm.hl.TZ0.2e: Find the maximum number of edges that can be added to the graph G (not including any loops or...
• SPNone.3dm.hl.TZ0.2a: Draw the graph G as a planar graph.
• 10N.3dm.hl.TZ0.5a: A graph has n vertices with degrees 1, 2, 3, …, n. Prove that \(n \equiv 0(\bmod 4)\) or...
• 11N.3dm.hl.TZ0.3a: In any graph, show that (i)     the sum of the degrees of all the vertices is even; (ii)    ...
• 11N.3dm.hl.TZ0.3b: Consider the following graph, M. (i)     Show that M is planar. (ii)     Explain why M is not...
• 10N.3dm.hl.TZ0.5b: Let G be a simple graph with n vertices, \(n \geqslant 2\). Prove, by contradiction, that at...
• 14M.3dm.hl.TZ0.1a: Draw the graph \(K\).
• 14M.3dm.hl.TZ0.3: (a)     Draw a spanning tree for           (i)     the complete graph, \({K_4}\);          ...
• 13N.3dm.hl.TZ0.2: The following figure shows the floor plan of a museum.   (a)     (i)     Draw a graph G that...
• 15N.3dm.hl.TZ0.4c: In a planar graph the degree of a face is defined as the number of edges adjacent to that...
• 15N.3dm.hl.TZ0.4d: \(H\) is a simple connected planar bipartite graph with \(e\) edges, \(f\) faces, \(v\) vertices...