Definition:Semi-Eulerian Graph
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Definition
A graph is called semi-Eulerian if and only if it contains an Eulerian trail.
Note that the definition of graph here includes:
Note that an Eulerian graph is also semi-Eulerian, as an Eulerian circuit is still a path, and therefore an Eulerian trail.
Examples
Arbitrary Example
The following is a semi-Eulerian graph:
An example of an Eulerian trail is:
- $A \to B \to C \to D \to E \to B \to C \to A \to E$
Also known as
A semi-Eulerian graph is also called a traversable graph.
Some sources have transversable graph but it is suspected that this is a mistake.
Also see
- Results about semi-Eulerian graphs can be found here.
Source of Name
This entry was named for Leonhard Paul Euler.
Sources
- 1977: Gary Chartrand: Introductory Graph Theory ... (previous) ... (next): $\S 3.1$: The Königsberg Bridge Problem: An Introduction to Eulerian Graphs
- 1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) ... (previous) ... (next): Eulerian graph
- 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) ... (previous) ... (next): Eulerian graph
- 2014: Christopher Clapham and James Nicholson: The Concise Oxford Dictionary of Mathematics (5th ed.) ... (previous) ... (next): transversable graph
- 2021: Richard Earl and James Nicholson: The Concise Oxford Dictionary of Mathematics (6th ed.) ... (previous) ... (next): traversable graph