hasEulerianTrail -- determines whether a graph or a digraph has an Eulerian trail

Synopsis

Usage:

E = hasEulerianTrail G

E = hasEulerianTrail D
Inputs:
- G, a graph,
- D, a digraph,
Outputs:
- E, a Boolean value, whether G or D has an Eulerian trail

Description

A graph has an Eulerian trail if there is a path in the graph that visits each edge exactly once. A digraph has a Eulerian trail if there is a directed path in the graph that visits each edge exactly once. An Eulerian trail is also called an Eulerian path. Unconnected graphs can have a Eulerian trail, but all vertices of degree greater than 0 of a graph (or all vertices of degree greater than 0 in the underlying graph of a digraph) must belong to a single connected component.

i1 : G = cycleGraph 5;

i2 : hasEulerianTrail G

o2 = true

i3 : D = digraph(toList(1..4), {{1,2},{2,3},{3,4}});

i4 : hasEulerianTrail D

o4 = true

Ways to use hasEulerianTrail :

hasEulerianTrail(Digraph)
hasEulerianTrail(Graph)

For the programmer

The object hasEulerianTrail is a method function.

hasEulerianTrail -- determines whether a graph or a digraph has an Eulerian trail

Synopsis

Description

See also

Ways to use hasEulerianTrail :

For the programmer