Pairs of graded graphs, together with the Fomin property of graded graph duality, are rich combinatorial structures providing among other a framework for enumeration. The prototypical example is the one of the Young graded graph of integer partitions, allowing us to connect number of standard Young tableaux and numbers of permutations. Here, we use operads, algebraic devices abstracting the notion of composition of combinatorial objects, to build pairs of graded graphs. For this, we first construct a pair of graded graphs where vertices are syntax trees, the elements of free nonsymmetric operads. This pair of graphs is dual for a new notion of duality called \(\phi \)-diagonal duality, similar to the ones introduced by Fomin. We also provide a general way to build pairs of graded graphs from operads, wherein underlying posets are analogous to the Young lattice. Some examples of operads leading to new pairs of graded graphs involving integer compositions, Motzkin paths, and m-trees are considered.

成对的渐变图以及渐变图对偶的Fomin属性是丰富的组合结构，除其他外，它还提供了枚举的框架。原型示例是整数分区的Young分级图之一，它使我们可以连接标准Young表格的数量和排列的数量。在这里，我们使用操作数，代数设备抽象组合对象组成的概念，以构建成对的渐变图。为此，我们首先构造一对渐变图，其中顶点是语法树，是自由非对称操作数的元素。这对图是对偶的，表示一个新的对偶概念，称为\（\ phi \）-对角二元性，类似于Fomin引入的对角二元性。我们还提供了一种从操作对象构建成对的渐变图对的通用方法，其中基础的位姿类似于Young格。考虑了一些导致整数图，Motzkin路径和m -tree的新的成对的梯度图对的操作实例。