Question

prove that Peterson's graph?using kutasowski's theorem show that the Peterson's graph are nonplanar​

Answer 1

Using your notation, we have that n=10, m=15. Inspecting the graph, we see that (1) each edge is included in exactly two faces, and (2) each cycle has a length of 5 or greater. Combining these two facts yields 5f≤2m. Substituting this into Euler's formula, we obtain a contradiction.