Definition:Adjacent (Graph Theory)/Vertices

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Definition

Undirected Graph

Let $G = \struct {V, E}$ be an undirected graph.

Two vertices $u, v \in V$ of $G$ are adjacent if there exists an edge $e = \set {u, v} \in E$ of $G$ to which they are both incident.


Digraph

Let $G = \struct {V, E}$ be a digraph.

Two vertices $u, v \in V$ of $G$ are adjacent if there exists an arc $e = \left({u, v}\right) \in E$ of $G$ to which they are both incident.


Non-Adjacent

Let $G = \struct {V, E}$ be a graph.

Two vertices $u, v \in V$ of $G$ are non-adjacent if they are not adjacent.


Sources