The Chmutov-Lando theorem claims that the value of a weight system (a function on the chord diagrams that satisfies the four-term Vassiliev relations) corresponding to the Lie algebra depends only on the intersection graph of the chord diagram.We compute the values of the weight system at the graphs in several infinite series, which are the joins of a graph with a small number of vertices and a discrete graph. In particular, we calculate these values for a series in which the initial graph is the cycle on five vertices; the graphs in this series, apart from the initial one, are not intersection graphs.We also derive a formula for the generating functions of the projections of graphs equal to the joins of an arbitrary graph and a discrete graph to the subspace of primitive elements of the Hopf algebra of graphs. Using the formula thus obtained, we calculate the values of the weight system at projections of the graphs of the indicated form onto the subspace of primitive elements. Our calculations confirm Lando’s conjecture concerning the values of the weight system at projections onto the subspace of primitives.Bibliography: 17 titles.

中文翻译：

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不是和弦图交集图的一组图上权重系统的值

Chmutov-Lando 定理声称对应于李代数的权重系统（弦图上满足四项 Vassiliev 关系的函数）的值 仅取决于和弦图的交集图。我们计算的值 几个无限级数图上的权重系统，这些级数是具有少量顶点的图和离散图的连接。特别是，我们为一个序列计算这些值，其中初始图是五个顶点上的循环；这个系列中的图，除了最初的那个，都不是交图。我们还推导出一个图的投影生成函数的公式，等于任意图和离散图到原始元素子空间的连接图的 Hopf 代数。使用由此获得的公式，我们计算的值 将指定形式的图形投影到原始元素的子空间上的权重系统。我们的计算证实了 Lando 关于 投影到基元子空间的权重系统。参考书目：17 个标题。