论文标题
常规图的不交互结合的通用光谱
Universal spectra of the disjoint union of regular graphs
论文作者
论文摘要
A universal adjacency matrix of a graph $G$ with adjacency matrix $A$ is any matrix of the form $U = αA + βI + γJ + δD$ with $α\neq 0$, where $I$ is the identity matrix, $J$ is the all-ones matrix and $D$ is the diagonal matrix with the vertex degrees.如果$ g $是常规图的不相交联合，我们就各种通用邻接矩阵的特征多项式表示了一个表达式，就组件的邻接矩阵的特征多项式而言。结果，我们获得了$ g $的seidel矩阵的特征多项式的公式，以及$ g $的补充的无价laplacian（即常规图的联接）。
A universal adjacency matrix of a graph $G$ with adjacency matrix $A$ is any matrix of the form $U = αA + βI + γJ + δD$ with $α\neq 0$, where $I$ is the identity matrix, $J$ is the all-ones matrix and $D$ is the diagonal matrix with the vertex degrees. In the case that $G$ is the disjoint union of regular graphs, we present an expression for the characteristic polynomials of the various universal adjacency matrices in terms of the characteristic polynomials of the adjacency matrices of the components. As a consequence we obtain a formula for the characteristic polynomial of the Seidel matrix of $G$, and the signless Laplacian of the complement of $G$ (i.e. the join of regular graphs).
