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In this paper, we characterize chordal and perfect zero-divisor graphs offinite posets. Also, it is proved that the zero-divisor graphs of finite posetsand the complement of zero-divisor graphs of finite $0$-distributive posetssatisfy the Total Coloring Conjecture. These results are applied to thezero-divisor graphs of finite reduced rings, the comaximal ideal graph ofrings, the annihilating ideal graphs, the intersection graphs of ideals ofrings, and the intersection graphs of subgroups of cyclic groups. In fact, itis proved that these graphs associated with a commutative ring $R$ withidentity can be effectively studied via the zero-divisor graph of a speciallyconstructed poset from $R$.

Coloring of zero-divisor graphs of posets and applications to graphs associated with algebraic structures