Definition:Degree (Vertex)

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Definition

Let $G = \left({V, E}\right)$ be an undirected graph.

Let $v \in V$ be a vertex of $G$.


The degree of $v$ in $G$ is the number of edges to which it is incident.

It is denoted $\deg_G \left({v}\right)$, or just $\deg \left({v}\right)$ if it is clear from the context which graph is being referred to.


That is:

$\deg_G \left({v}\right) = \left|{\left\{{u \in V : \left\{{u, v}\right\} \in E}\right\}}\right|$.


Even Vertex

If the degree of $v$ is even, then $v$ is called an even vertex.


Odd Vertex

If the degree of $v$ is odd, then $v$ is an odd vertex.


Isolated Vertex

If the degree of $v$ is zero, then $v$ is an isolated vertex.


Also see


Sources