On powering adjacency and antiadjacency matrices of a directed graph.

Adjacency and antiadjacency matrices are the representation matrices of a directed graph. From the earlier papers, its have been known that the powering of the adjacency matrix of a directed graph can be used to find the number of directed paths and cycles. However, we found that there is a case in which the theorem does not work. Therefore, in this paper, we will extend the powering of the adjacency matrix of a directed graph and also give the additional requirement so that the properties are worked. We also generalized the case for a general directed graph, which means the graph might have loop(s) and digon(s). On the other hand, we also give the representation of the powering of the antiadjacency matrix. [ABSTRACT FROM AUTHOR]