Question

8. Determine whether each graph is planar. If the graph is planar, redraw it so that no edges cross; otherwise, find a subgraph homeomorphic to either K5 or K3,3 (a) (10 pts) See Figure in 3. (b) (5 pts) See Figure in 4 Figure 3: Graph for Question 8(a) مل a e С Figure 4: Graph for Question 8(b)

Answer 1

it CYOSS On that other Do each at Let us there is to Some graph G is said to be planar if can be dracon a plane so two edges non-verlex point: go through Some definitions. In graph theory, noo graphs G and a are homeomorphic, if a graph isomorphism from some subdivision of G Subdivision of G'. In general, a Subdivision of a graph G i a graph resulting from the Subdivision of edges in G. The subdivision of edges her to e with end points fu.v} yields a graph containing vertex w and with an edge ser replacing e by new edges fu,w and {w,v}. For two edges e, fez egi Conneckng to doow fig 3 8(a) and the graph. one neo iolo e can be subdivided V ez New verten w. Name (a) Ler 12 5 2 10 & 9 3 4 (G) graph G a For that we are a Subdivision 13,3" has The to conss der verlex set the vertices 1,8,9 going as another look at the vertex set & let us and 2,5,6 figure.

5 6 2 O 3 9 8 clearly this graph ý homeomorphic the given graph G ůs to K3,3. So by kurahisw kis non-planar. theorem (b) Now consider 5g 4 816) a ch b d. с Let us re-draw the graph. $ е. C d clearly no each other at a non-Vertex too edges cross point to this graph is planar.
the first graph is non planar and the second graph is planar.