Theorem 5.4: Let 8(G22, then there is a simple circuit in the graph G Proof: If graph G contains loops or multiple edges, then there is a simple circuit.(a, a)or(e, e"). Let g be a simple graph For any vertex vo of G, god(vo22, next vertex, adjacent, Pigeonhole pl rinciple❖ Theorem 5.4:Let  (G)≥2, then there is a simple circuit in the graph G. ❖ Proof: If graph G contains loops or multiple edges, then there is a simple circuit. (a,a) or (e,e'). ❖ Let G be a simple graph. For any vertex v0 of G, ❖ d(v0 )≥2, next vertex, adjacent, Pigeonhole principle