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 |
The object isEulerian is a method function.