# Definition:Even Vertex (Graph Theory)

Jump to navigation
Jump to search

## Contents

## 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:

## Also see

## Sources

- 1977: Gary Chartrand:
*Introductory Graph Theory*... (previous) ... (next): Chapter $2$: Elementary Concepts of Graph Theory: $\S 2.1$: The Degree of a Vertex - 1992: George F. Simmons:
*Calculus Gems*... (previous) ... (next): Chapter $\text {A}.21$: Euler ($\text {1707}$ – $\text {1783}$)