Math137a Final& Exam,& June& 9Th,& 2022 1. & Show& That& If& A& Connected& Graph& On& N& Vertices& Has& N + 1& Edges,& Then& It& Must& Have& At& Least& Two& Cycles.2. & Draw& All& Graphs& (Up& To& Isomorphism)& With& 5& Vertices& An

Math137a Midterm -& April& 29Th,& 2022 1.& & & (A) & Draw& A& Single& Simple& Graph& That& Simultaneously& Has& The& Following& Properties:I.& Is& Planar.Ii. & Has& Two& Edge-Disjoint& Hamiltonian& Cycles.Iii.& Is& Not& Eulerian.(B) & For& Yo