In this paper, we prove that the study of the subgraph \(T(Z^*(L))\) of the total graph T(L) of a lattice L is essentially the study of the zero-divisor graph of a poset. Also, we prove that the graph \(T^c(Z^*(L))\) is weakly perfect whereas \(T(Z^*(L))\) is not weakly perfect. The graph \(T(Z^*(L))\) and its complement \(T^c(Z^*(L))\) are shown to be a perfect graph if and only if L has at most four atoms. In the concluding section, we establish that, in the context of a commutative reduced ring R, the total graph, the annihilating ideal graph, the complement of the co-annihilating ideal graph, and the complement of the comaximal ideal graph coincide.

在本文中，我们证明了格子L的总图T ( L )的子图\(T(Z^*(L))\)的研究本质上是偏序集的零除数图的研究。此外，我们证明图\(T^c(Z^*(L))\)是弱完美的，而\(T(Z^*(L))\)不是弱完美的。当且仅当L最多有四个原子时，图\(T(Z^*(L))\)及其补图\(T^c(Z^*(L))\)被证明是完美图。在结论部分，我们确定，在交换约简环R的背景下，全图、理想理想图湮灭、共湮理想图的补和共极大理想图的补是一致的。