The class of unicyclic non-bipartite graphs with unique perfect matching, denoted by $\mathcal{U}$, is considered in this article. This article provides a complete characterization of unicyclic graphs in $\mathcal{U}$ which possess tricyclic inverses.

中文翻译：

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在具有三环逆元的单环非二部图上

具有唯一完美匹配的单环非二部图类，表示为$\mathcal{ü}$, 在本文中被考虑。本文提供了单环图的完整表征$\mathcal{ü}$具有三环逆元。