Are the following graphs planar? If so, show a planar representation and if not, explain why not. ь. Are the following graphs planar? If so, show a planar representation and if not, explain why...
For each of the following graphs draw a planar representation or show that it has a subgraph homeomorphic to K5 or K3,3: For each of the following graphs draw a planar representation or show that it has a subgraph homeomorphic to K; or K3,3: (a) (b) (c) (d)
3. For each of the following graphs, determine if the graph is planar. If it is, draw a plane representation of the graph; if not, indicate a subgraph homeomorphic to Kor K3,3 G
Determine if each of the following graphs is planar. Graph G1: [ Select ] ["Non-planar", "Planar"] Graph G2: [ Select ] ["Planar", "Non-planar"] Graph G3: [ Select ] ["Non-planar", "Planar"] ...
Show that the following graph is planar by redrawing it so that no edges cross each other.
(2) [20 ptsl Which of the following pairs of graphs are isomorphic? Explain why (2) [20 ptsl Which of the following pairs of graphs are isomorphic? Explain why
3. Which of the following graphs are planar? Find K 3.3 or Ks configurations in the nonplanar graphs (almost all are K3,3). (k) (1)
are your graphs linear? If so, why? If not, why not?
Use the outline of the chair conformation to draw a correct representation of the planar structure. You must show all atoms (including hydrogen atoms) in their correct axial or equatorial positions. - - - - - -
8. The thickness θ(G) of a graph is the minimum number of planar graphs whose union is G (Hence θ(G)-1 if and only if G is planar.) For a simple (p, q)-graph G, show that θ(G) 3 1 8. The thickness θ(G) of a graph is the minimum number of planar graphs whose union is G (Hence θ(G)-1 if and only if G is planar.) For a simple (p, q)-graph G, show that θ(G) 3 1