THE RELATION BETWEEN TOPOLOGICAL ORDERING AND ADJACENCY MATRIX IN DIGRAPHS
محورهای موضوعی : فصلنامه ریاضی
T. Rastad
1
(Islamic Azad University, Central Tehran Branch, Tehran, Iran.
Iran, Islamic Republic of
Department of Mathematics)
N. Delfan
2
(Islamic Azad University, Central Tehran Branch, Tehran, Iran.
Iran, Islamic Republic of
Department of Mathematics)
کلید واژه: adjacency matrix, topological ordering, acyclic digraph,
چکیده مقاله :
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.
