论文标题
$α$ -HERMITIAN邻接矩阵的倒数矩阵
Inverse of $α$-Hermitian Adjacency Matrix of a Unicyclic Bipartite Graph
论文作者
论文摘要
令$ x $为双方混合图，对于单位复数数字$α$，$h_α$是其$α$ -HERMITIAN邻接矩阵。如果$ x $具有独特的完美匹配，则$h_α$具有hermitian倒数$h_α^{ - 1} $。在本文中，我们在顶点之间的路径方面对$h_α^{ - 1} $的条目进行了完整描述。此外，$α$等于unity $γ$的原始第三根根，对于独特的完美匹配，对于独特的二键图$ x $，我们表征$h_γ^{ - 1} $ as $ \ pm 1 $ diagonall diagonally diagonally类似于$γ$γ$ -Hermitian邻接矩阵的混合图。通过我们的工作，我们为$ \ pm 1 $对角线矩阵提供了新的建筑。
Let $X$ be bipartite mixed graph and for a unit complex number $α$, $H_α$ be its $α$-hermitian adjacency matrix. If $X$ has a unique perfect matching, then $H_α$ has a hermitian inverse $H_α^{-1}$. In this paper we give a full description of the entries of $H_α^{-1}$ in terms of the paths between the vertices. Furthermore, for $α$ equals the primitive third root of unity $γ$ and for a unicyclic bipartite graph $X$ with unique perfect matching, we characterize when $H_γ^{-1}$ is $\pm 1$ diagonally similar to $γ$-hermitian adjacency matrix of a mixed graph. Through our work, we have provided a new construction for the $\pm 1$ diagonal matrix.
