A graph $G$ is factored into graphs $H$ and $K$ via a matrix product if there exist adjacency matrices $A$, $B$, and $C$ of $G$, $H$, and $K$, respectively, such that $A = BC$. In this paper, we study the spectral aspects of the matrix product of graphs, including regularity, bipartiteness, and connectivity. We show that if a graph $G$ is factored into a connected graph $H$ and a graph $K$ with no isolated vertices, then certain properties hold. If $H$ is non-bipartite, then $G$ is connected. If $H$ is bipartite and $G$ is not connected, then $K$ is a regular bipartite graph, and consequently, $n$ is even. Furthermore, we show that trees are not factorizable, which answers a question posed by Maghsoudi et al.

翻译：若图$G$的邻接矩阵$A$可表示为图$H$的邻接矩阵$B$与图$K$的邻接矩阵$C$的乘积，即$A = BC$，则称图$G$可通过矩阵乘积分解为图$H$和$K$。本文研究了图矩阵乘积的谱性质，包括正则性、二分性与连通性。我们证明：若图$G$可分解为一个连通图$H$与一个无孤立顶点的图$K$，则以下性质成立：若$H$为非二分图，则$G$连通；若$H$为二分图且$G$不连通，则$K$为正则二分图，此时顶点数$n$为偶数。此外，我们证明了树结构不可因子化，这回答了Maghsoudi等人提出的一个问题。