A little more on the zero-divisor graph and the annihilating-ideal graph of a reduced ring

We have tried to translate some graph properties of AG® and Gamma® to the topological properties of Zariski topology. We prove that Rad(Gamma®) and Rad(AG®) are equal and they are equal to 3, if and only if the zero ideal of R is an anti fixed-place ideal, if and only if Min® does not have any isolated point, if and only if Gamma® is triangulated, if and only if AG® is triangulated. Also, we show that if the zero ideal of a ring R is a fixed-place ideal, then dtt(AG®) = |B®| and also if in addition |Min®| > 2, then dt(AG®) = |B®|. Finally, it has been shown that dt(AG®) is finite, if and only if dtt(AG® is finite; if and only if Min® is finite.