DP Mathematics HL Questionbank

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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...
• 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.TZ2.2b: Show that a graph cannot have exactly one vertex of odd degree.
• 11N.3dm.hl.TZ0.3a: In any graph, show that (i)     the sum of the degrees of all the vertices is even; (ii)    ...
• 15M.3dm.hl.TZ0.4b: (i)     State the handshaking lemma. (ii)     Determine the value of $f$, if each vertex has...
• 14N.3dm.hl.TZ0.2c: Explain why each person cannot have shaken hands with exactly nine other people.