Islamic Azad University, Central Tehran Branch, Tehran, Iran. Iran, Islamic Republic of Department of Mathematics
In this paper the properties of node-node adjacency matrix in acyclic digraphs are considered. It is shown that topological ordering and node-node adjacency matrix are closely related. In fact, first the one to one correspondence between upper triangularity of node-node adjacency matrix and existence of directed cycles in digraphs is proved and then with this correspondence other properties of adjacency matrix in acyclic digraphs are presented.