Definition:Even Vertex of Graph

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

• Definition:Odd Vertex of Graph

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 ($\text {1707}$ – $\text {1783}$)
• 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): graph: 2.
• 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): graph: 2.