The IsEulerian command returns true if the input graph is an Eulerian graph, i.e there exists a closed walk in the graph that uses each edge exactly once. It returns false otherwise.

An optional second argument T is assigned an Eulerian Trail of the graph if such a trail exists, and FAIL otherwise.

The algorithm used to construct the Eulerian trail is depth-first-search. The complexity is  where n=|V| and m=|E|.