论文标题
正交对称矩阵和图的连接
Orthogonal symmetric matrices and joins of graphs
论文作者
论文摘要
我们引入了多种矩阵的兼容性概念。这引起了两个（可能是断开连接的）图$ g $和$ h $的连接的必要条件，以作为正交对称矩阵的模式，或等效地，对于$ g \ vee h $的最小数量的不同eigenValues $ q $等于两个。在其他假设下，我们表明这种必要条件也足够。作为一个应用程序，我们证明$ q（g \ vee h）$是$ g $和$ h $是完整图的工会时，我们在每种情况发生时表征。
We introduce a notion of compatibility for multiplicity matrices. This gives rise to a necessary condition for the join of two (possibly disconnected) graphs $G$ and $H$ to be the pattern of an orthogonal symmetric matrix, or equivalently, for the minimum number of distinct eigenvalues $q$ of $G\vee H$ to be equal to two. Under additional hypotheses, we show that this necessary condition is also sufficient. As an application, we prove that $q(G\vee H)$ is either two or three when $G$ and $H$ are unions of complete graphs, and we characterise when each case occurs.
