A noneulerian graph is a graph that is not Eulerian. The numbers of simple noneulerian graphs on 
, 2, ... nodes are 2, 3, 10, 30, 148, 1007, 12162, 272886,
... (OEIS A145269), and the corresponding numbers
of simple connected noneulerian graphs are 0, 1, 1, 5, 17, 104, 816, 10933, 259298,
... (OEIS A158007).
Any graph with a vertex of odd degree or a bridge is noneulerian.
