## Question

###### In class. We used counting argument to prove that K33 is nonplanar. Modify the argument appropriately to prove that the Petersen graph (Figure 2.6, p.39) nonplanar. Give an example or explain why none exists_ If giving an example, be sure to justify why vour example satisfies the given criteria: planar graph with degree sequence 403),5(),6(3) , 7(3) planar 4-regular graph nonplanar A-regular graph K , Suppose T is a (ree)offorder (a) Find the order and size of the graph T + T. Express YOur an

In class. We used counting argument to prove that K33 is nonplanar. Modify the argument appropriately to prove that the Petersen graph (Figure 2.6, p.39) nonplanar. Give an example or explain why none exists_ If giving an example, be sure to justify why vour example satisfies the given criteria: planar graph with degree sequence 403),5(),6(3) , 7(3) planar 4-regular graph nonplanar A-regular graph K , Suppose T is a (ree)offorder (a) Find the order and size of the graph T + T. Express YOur answers in terms of k. Include couple of sentences explaining the reasoning behind your formulas (b) Prove that if k23 then T + T is nonplanar Prove that there is no connected planar graph that is 4-regular and has seven regions_ (Note: Your proof must work for arbitrary number of vertices S0 in your proof, let n denote the number of vertices: