# Definition:Even Vertex (Graph Theory)

## Definition

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

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

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

## Examples

### Graph with All Even Vertices

Examples of simple graphs whose vertices are all even include the cycle graphs.

For example, the cycle graph of order $4$:

### Graph with One Even Vertex

The following is an example of a simple graph with exactly one even vertex:

### Graph with $2$ Even Vertices

An example of a simple graph with $2$ even vertices: