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...
• 12M.3dm.hl.TZ0.4b: A simple graph G has v vertices and e edges. The complement $G'$ of G has ${e'}$ edges. (i)...
• 08M.3dm.hl.TZ2.5: (a)     (i)     Show that Euler’s relation $f - e + v = 2$ is valid for a spanning tree of...
• 10M.3dm.hl.TZ0.4: (a)     Show that, for a connected planar graph, $$v + f - e = 2.$$ (b)     Assuming that...
• 10N.3dm.hl.TZ0.1b: (i)     A graph is simple, planar and connected. Write down the inequality connecting v and e,...
• 15N.3dm.hl.TZ0.4e: Hence prove that for $H$ (i)     $e \ge 2f$; (ii)     $e \le 2v - 4$.
• 15N.3dm.hl.TZ0.4f: Hence prove that ${K_{3,{\text{ }}3}}$ is not planar.
• 15M.3dm.hl.TZ0.4a: (i)     Show that $2e \ge 3f{\text{ if }}v > 2$. (ii)     Hence show that ${K_5}$, the...
• 15M.3dm.hl.TZ0.4b: (i)     State the handshaking lemma. (ii)     Determine the value of $f$, if each vertex has...