Neighbourhood

Builds on Graph

Definition

Let $G$ be a graph with vertex set $V$ , and let $v \in V$ . The neighbourhood of $v$ is the set $N(v) = \{ u \in V : u \sim v \}$ of the vertices adjacent to $v$ . The elements of $N(v)$ are the neighbours of $v$ .

Remarks

This is the open neighbourhood. It does not contain $v$ , because no vertex is adjacent to itself. The closed neighbourhood is $N[v] = N(v) \cup \{v\}$ . The degree of $v$ is $|N(v)|$ when $N(v)$ is finite. In the cycle with vertices $1, 2, 3, 4, 5$ in this order, $N(1) = \{2, 5\}$ .

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Graph definition
Neighbourhood definition

Tag	`01T3TMGTTE`
URI	`m2://01T3TMGTTE`
Kind	definition
Writing	W0 stub
MSC	05C07
Defines	Neighbourhood
Uses	Graph

Neighbourhood

Definition

Remarks

Reading path

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