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