A graph is supereulerian if it contains a spanning closed trail. We prove several Erds-type extremal size conditions with a lower bounded minimum degree for a graph to be supereulerian and with different edge-connectivity, with the corresponding extremal graphs characterized. These results are then applied to prove sufficient conditions involving adjacency spectral radius and signless Laplacian spectral radius for a graph to be supereulerian.

中文翻译：

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超欧拉图的谱和极值条件

如果图包含跨越闭合路径，则该图是超欧拉图。我们证明了几个 Erds 型极值尺寸条件，其中图的下界最小度为超欧拉且具有不同的边连通性，并具有相应的极值图特征。然后应用这些结果来证明包含邻接谱半径和无符号拉普拉斯谱半径的充分条件，使图成为超欧拉图。