Directed prime graph of non-commutative ring

Prime graph of a ring R is a graph whose vertex set is the whole set R any any two elements x and y of R are adjacent in the graph if and only if xRy = ۰ or yRx = ۰.  Prime graph of a ring is denoted by PG(R). Directed prime graphs for non-commutative rings and connectivity in the graph are studied in the present paper. The diameter and girth of this graph are also studied in the paper.

کلیدواژه ها:

Prime graph ، Non-commutative Ring ، Directed Graph