Definition:Even Vertex (Graph Theory)

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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 $4$:

C4.png


Graph with One Even Vertex

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

OneEvenVertex.png


Graph with $2$ Even Vertices

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

Chartrand-exercise-2-1-7ef.png


Also see


Sources