yields True if the graph g is Eulerian, and False otherwise.
Examplesopen allclose all
Basic Examples (2)
EulerianGraphQ works with undirected graphs:
EulerianGraphQ gives False for expressions that are not graphs:
EulerianGraphQ works with large graphs:
Find if the the seven bridges of the city of Königsberg over the river Pregel can all be traversed in a single trip without doubling back, with the additional requirement that the trip end in the same place it began:
Test whether the figure of an envelope can be traced without lifting the pen and without going over the same line twice:
A scheduling of a conference room and the corresponding graph of participants with edges between attendees of the same meeting:
Test whether two consecutive meetings can share a participant:
Properties & Relations (7)
An Eulerian cycle can be found using FindEulerianCycle:
A connected undirected graph is Eulerian iff every graph vertex has an even degree:
A connected undirected graph is Eulerian if it can be decomposed into edge disjoint cycles:
The graphs are cycles if they are connected and have an equal number of edges and vertices:
For connected directed graphs:
The line graph of an undirected Eulerian graph is Eulerian:
The line graph of an Eulerian graph is Hamiltonian:
A connected directed graph is Eulerian iff every vertex has equal in-degree and out-degree:
Wolfram Research (2010), EulerianGraphQ, Wolfram Language function, https://reference.wolfram.com/language/ref/EulerianGraphQ.html.
Wolfram Language. 2010. "EulerianGraphQ." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/EulerianGraphQ.html.
Wolfram Language. (2010). EulerianGraphQ. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/EulerianGraphQ.html