Definition:Adjacent (Graph Theory)/Edges

Definition

Undirected Graph

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

Two edges $e_1, e_2 \in E$ of $G$ adjacent if and only if there exists a vertex $v \in V$ to which they are both incident.

Digraph

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

Two arcs $e_1, e_2 \in E$ of $G$ adjacent if and only if there exists a vertex $v \in V$ to which they are both incident.

Non-Adjacent

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

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

Also known as

Adjacent edges of a graph can also be described as neighboring (British English spelling: neighbouring).

Some sources use the term coterminal.

Also see

• Results about adjacency in the context of graph theory can be found here.

Sources

• 1989: Ephraim J. Borowski and Jonathan M. Borwein: Dictionary of Mathematics ... (previous) ... (next): adjacent: 1. b. (of a pair of edges in a graph)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): coterminal: 2.
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): graph: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): coterminal: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): graph: 2.
• 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): adjacent edges