THE CENTRAL VERTICES an‎d RADIUS OF THE REGULAR GRAPH OF IDEALS

The regular graph of ideals of the commutative ring R, denoted by reg(R), is a graph whose vertex set is the set of all non-trivial ideals of R and two distinct vertices I and J are adjacent if and only if either I contains a J-regular element or J contains an I-regular element. In this paper, it is proved that the radius of reg(R) equals 3. The central vertices of reg(R) are determined, too.