s Proof: (l)Let connected multigraph G have an Euler circuit. then each of its vertices has even degree. ☆(VaV 09V19°·9i.9Vk9v0k First note that an Euler circuit begins with a vertex Vo and continues with an edge incident to Vo, say & V1. The edge (vo, v1 contributes one to d(vo) 8. Thus each of g's vertices has even degree.❖Proof:(1)Let connected multigraph G have an Euler circuit, then each of its vertices has even degree. ❖ (v0 ,v1 ,…,vi , …,vk ),v0=vk ❖First note that an Euler circuit begins with a vertex v0 and continues with an edge incident to v0 , say {v0 ,v1 }. The edge {v0 ,v1 } contributes one to d(v0 ). ❖ Thus each of G’s vertices has even degree