论文标题
才华横溢的单体和Leavitt Path代数的邻接矩阵观点
An Adjacency Matrix Perspective of Talented Monoids and Leavitt Path Algebras
论文作者
论文摘要
在本文中，我们建立了Leavitt Path代数，才华横溢的单体和基础图的邻接矩阵之间的关系。我们表明，实际上，邻接矩阵在某种意义上产生了对才华横溢的Monoid发电机的群体行动。在此的帮助下，我们通过才华横溢的Monoid推断出图形的多个图形指数的形式。我们通过邻接矩阵对遗传和饱和子集进行了分类。此外，我们给出一个公式，以根据邻接矩阵计算LEAVITT路径代数中给定长度的所有路径。此外，我们讨论了图中的循环数量。特别是，我们通过邻接矩阵，才华横溢的Monoid和Leavitt Path代数对链球图进行了等效的表征。
In this article we establish relationships between Leavitt path algebras, talented monoids and the adjacency matrices of the underlying graphs. We show that indeed the adjacency matrix generates in some sense the group action on the generators of the talented monoid. With the help of this we deduce a form of the aperiodicity index of a graph via the talented monoid. We classify hereditary and saturated subsets via the adjacency matrix. Moreover we give a formula to compute all paths of a given length in a Leavitt path algebra based on the adjacency matrix. In addition we discuss the number of cycles in a graph. In particular we give an equivalent characterization of acylic graphs via the adjacency matrix, the talented monoid and the Leavitt path algebra.
