Definition:Degree (Vertex)

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Definition

Let $G = \struct {V, E}$ 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 $\map {\deg_G} v$, or just $\map \deg v$ if it is clear from the context which graph is being referred to.


That is:

$\map {\deg_G} v = \card {\set {u \in V : \set {u, v} \in E} }$


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