This article provides a combinatorial description of the inverse of the adjacency matrix of a non-singular 3-coloured digraph. The class of unicyclic 3-coloured digraphs with the cycle weight ±i and with a unique perfect matching, denoted by ${\mathcal{U}}_g$, is considered in this article. We characterize the 3-coloured digraphs in ${\mathcal{U}}_g$ whose inverses are again 3-coloured digraphs. Furthermore, the 3-coloured digraphs in ${\mathcal{U}}_g$ whose inverses are bipartite are also characterized. It is proved that the inverses of the 3-coloured digraphs in ${\mathcal{U}}_g$ are always Laplacian non-singular. Characterizations of unicyclic 3-coloured digraphs in ${\mathcal{U}}_g$ possessing unicyclic inverses are also supplied in this article. As an application, we can obtain the class of unicyclic 3-coloured digraphs with the cycle weight ±i satisfying the strong reciprocal eigenvalue property.

本文提供了非奇异三色有向图的邻接矩阵逆矩阵的组合描述。循环权重为±i且具有唯一完美匹配的单环三色有向图类，表示为${\mathcal{ü}}_G$, 在本文中被考虑。我们将 3 色有向图的特征描述为${\mathcal{ü}}_G$其逆又是三色有向图。此外，中的 3 色有向图${\mathcal{ü}}_G$其逆是二分的也有特征。证明了中的三色有向图的逆${\mathcal{ü}}_G$总是拉普拉斯非奇异的。中单环三色有向图的特征${\mathcal{ü}}_G$本文还提供了拥有单环逆元。作为一个应用，我们可以获得循环权重±i满足强倒数特征值性质的单环三色有向图类。