Complete Bipartite Graph
# Definition
Let $G=(V, E)$ be a Bipartite Graph with partition ${A, B} \subset \mathcal{P}(V)$. Then we say that $G$ is a Complete Bipartite Graph if $$E = {{u, v} \in \mathcal{P}(V) : u \in A, v \in B}.$$ If $V = [n]$ for some $n \in \mathbb{N}$, then we notate $G = B_{n}$.