Definition:Even Vertex of Graph
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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 $4$:
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 ($\text {1707}$ – $\text {1783}$)
- 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.