isEulerian -- determines if a graph or digraph is Eulerian

Synopsis

Usage:

E = isEulerian G

E = isEulerian D
Inputs:
- G, a graph,
- D, a digraph,
Outputs:
- E, a Boolean value, whether G or D is Eulerian

Description

A graph is Eulerian if it has a path in the graph that visits each vertex exactly once. A digraph is Eulerian if it has a directed path in the graph that visits each vertex exactly once. Such a path is called an Eulerian circuit. Unconnected graphs can be Eulerian, 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 : bridges = graph ({{0,1},{0,2},{0,3},{1,3},{2,3}}, EntryMode => "edges");

i2 : E = isEulerian bridges

o2 = false

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

i4 : E = isEulerian D

o4 = true

Ways to use isEulerian :

isEulerian(Digraph)
isEulerian(Graph)

For the programmer

The object isEulerian is a method function.

isEulerian -- determines if a graph or digraph is Eulerian

Synopsis

Description

See also

Ways to use isEulerian :

For the programmer