Triameter of the zero divisor graph of a commutative ring with identity

The triameter of a connected graph [Formula: see text], [Formula: see text], is defined as the maximum of distance between three vertices [Formula: see text] and [Formula: see text] in graph, [Formula: see text]. The zero divisor graph, [Formula: see text], of a commutative ring [Formula: see text], is a graph in which the vertices represent the nonzero zero divisors of [Formula: see text] and two vertices are connected by an edge if and only if their product equals zero. In this paper, we determine the triameter of the zero divisor graph of a commutative ring. More specifically, we prove that the zero divisor graph does not have a triameter of five or seven. Further, we show that for any zero divisor graph, the triameter is always less than or equal to nine. In addition, we provide some characteristics of the triameter of [Formula: see text] and the characteristics of the elements in a triametral triple.