Let G be a graph having a unique perfect matching M, $A\left(G\right)$ be the adjacency matrix of G and $W\left(G\right)$ be the collection of all positive weight functions defined on the edge set of G in which each weight function w assigns weight 1 to each matching edge and a positive weight to each non-matching edge. The weighted graph $G_w$ satisfies the $(-SR)$ property if for each eigenvalue of $G_w$, its anti-reciprocal is also an eigenvalue of $G_w$ with the same multiplicity. In this paper, a class of graphs with a unique perfect matching M for which the diagonal entries of the inverse of the adjacency matrix of each graph are all zero is investigated. Furthermore, it is shown that no noncorona graph in this class satisfies the $(-SR)$ property even for a single weight function $w\in W\left(G\right)$.

令G为具有唯一完美匹配M的图，$\mathrm{一个}\left(G\right)$是G的邻接矩阵和$W\left(G\right)$是在G的边集上定义的所有正权重函数的集合，其中每个权重函数w将权重 1 分配给每个匹配的边，并将正权重分配给每个不匹配的边。加权图$G_w$满足$(-\mathrm{小号}R)$属性 if 对于每个特征值$G_w$, 它的反倒数也是一个特征值$G_w$具有相同的多重性。本文研究了一类具有唯一完美匹配M的图，其中每个图的邻接矩阵的逆矩阵的对角线元素都为零。此外，表明该类中没有非电晕图满足$(-\mathrm{小号}R)$即使对于单个权重函数也具有属性$w\in W\left(G\right)$.