The class of non-bipartite unicyclic graphs with a unique perfect matching, denoted by $\mathcal{U}$, is considered in this article. This article describes the entries of the inverse of the adjacency matrix of a graph in $\mathcal{U}$. It is proved that the inverse graph of a graph in $\mathcal{U}$ is always non-bipartite. In this article, we characterize the graphs in $\mathcal{U}$ whose inverses are mixed graphs. Among all such graphs in $\mathcal{U}$ we identify those graphs whose inverses are quasi-bipartite. Furthermore, characterizations of unicyclic graphs in $\mathcal{U}$ possessing unicyclic and bicyclic inverses are also provided in this article.

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具有唯一完美匹配的非二部单环图的逆

具有唯一完美匹配的非二部单环图类，记为$\mathcal{ü}$, 本文考虑。本文描述了图的邻接矩阵逆的条目$\mathcal{ü}$. 证明了图的逆图$\mathcal{ü}$总是非二分的。在本文中，我们描述了图$\mathcal{ü}$其逆是混合图。在所有这些图表中$\mathcal{ü}$我们识别那些逆是准二分的图。此外，单环图的表征$\mathcal{ü}$本文还提供了具有单环和双环逆的情况。