A complex unit gain graph is a triple $\mathrm{\Phi }=(G,\mathbb{T},\phi )$ (or $G^{\phi }$ for short) consisting of a simple graph G, as the underlying graph of $G^{\phi }$, the set of unit complex numbers $\mathbb{T}=\{z\in \mathbb{C}:|z|=1\}$ and a gain function $\phi :\overrightarrow{E}\to \mathbb{T}$ such that $\phi \left(e_{i,j}\right)=\phi (e_{j,i}{)}^{-1}$. Let $A\left(G^{\phi }\right)$ be the adjacency matrix of $G^{\phi }$. In this paper, we prove that $\begin{array}{rl}& m\left(G\right)-c\left(G\right)\le p\left(G^{\phi }\right)\le m\left(G\right)+c\left(G\right),\\ & m\left(G\right)-c\left(G\right)\le n\left(G^{\phi }\right)\le m\left(G\right)+c\left(G\right),\end{array}$where $p\left(G^{\phi }\right)$, $n\left(G^{\phi }\right)$, $m\left(G\right)$ and $c\left(G\right)$ are the number of positive eigenvalues of $A\left(G^{\phi }\right)$, the number of negative eigenvalues of $A\left(G^{\phi }\right)$, the matching number and the cyclomatic number of G, respectively. Furthermore, we characterize the graphs which attain the upper bounds and the lower bounds, respectively.

一个复杂的单位增益图是一个三重$\mathrm{\Phi }=(G,\mathbb{吨},\phi )$（或者$G^{\phi }$简而言之）由一个简单的图G组成，作为的基础图$G^{\phi }$, 单位复数集$\mathbb{吨}=\{z\in \mathbb{C}:|z|=\mathrm{1个}\}$和增益函数$\phi :\overrightarrow{乙}\to \mathbb{吨}$这样$\phi \left({\mathrm{电子}}_{我,j}\right)=\phi ({\mathrm{电子}}_{j,我}{)}^{-\mathrm{1个}}$. 让$A\left(G^{\phi }\right)$是邻接矩阵$G^{\phi }$. 在本文中，我们证明$\begin{array}{rl}& 米\left(G\right)-C\left(G\right)\le p\left(G^{\phi }\right)\le 米\left(G\right)+C\left(G\right),\\ & 米\left(G\right)-C\left(G\right)\le n\left(G^{\phi }\right)\le 米\left(G\right)+C\left(G\right),\end{array}$在哪里$p\left(G^{\phi }\right)$,$n\left(G^{\phi }\right)$,$米\left(G\right)$和$C\left(G\right)$是正特征值的数量$A\left(G^{\phi }\right)$，负特征值的数量$A\left(G^{\phi }\right)$，分别是G的匹配数和圈数。此外，我们分别描述了达到上限和下限的图。