Regular graph

A regular graph is a graph where each vertex has the same number of neighbors; i.e. every vertex has the same degree. regular graph with vertices of degree $k$ is called a $k$‑regular graph or regular graph of degree $k$.

• from the Handshaking lemma, a regular graph contains an even number of vertices with odd degree.
• Regular Bipartite graph has a Perfect matching. ^[C3.Q2a]
• number of edges in $k$‑regular graph with $n$ vertices is $\frac{nk}{2}$
• (question 5) - let $G=(V,E)$ regular graph. if $|V|$ is odd, then $G$ or $\overline{G}$ is Eulerian graph