Adjacent Vertex

Definition

Adjacent Vertex

Let $G=(V,E)$ be a graph. A vertex $u\in V$ is called adjacent to vertex $v\in V$, denoted as $u\sim v$, if there exists an edge connecting $u$ and $v$, i.e.,

$$u\sim v:⟺\exists e\in E:e\cap u=\{v\}.$$