Vertex

Topics: Graph Theory

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(definition)

In a graph, the points that represent elements are called vertices or nodes. The set of vertices in a graph, commonly denoted by $V$, must be non-empty.

An edge joins two vertices. Vertices have open and closed neighbourhoods.

Adjacency and Neighbours

When a vertex $v_1$ is joined to another vertex $v_2$ by means of an edge, we say that they’re adjacent and that $v_1$ is a neighbour of $v_2$.

Types §

An isolated vertex is a vertex with degree 0.

A hanging vertex is a vertex with degree 1.