A noneulerian graph is a graph that is notEulerian. The numbers of simple noneulerian graphs on, 2, ... nodes are 2, 3, 10, 30, 148, 1007, 12162, 272886, ... (OEISA145269), and the corresponding numbers of simple connected noneulerian graphs are 0, 1, 1, 5, 17, 104, 816, 10933, 259298, ... (OEISA158007).

Any graph with a vertex of odd degree or a bridge is noneulerian.

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Weisstein, Eric W. "Noneulerian Graph."FromMathWorld--A Wolfram Resource.https://mathworld.wolfram.com/NoneulerianGraph.html

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