DP Mathematics HL Questionbank
Handshaking lemma.
Description
[N/A]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.
