论文标题
顶点加权的Tutte对称函数，并具有相等的色度对称函数的构造图
A Vertex-Weighted Tutte Symmetric Function, and Constructing Graphs with Equal Chromatic Symmetric Function
论文作者
论文摘要
本文有两个主要部分。首先，我们考虑Tutte对称函数$ XB $，这是色度对称函数的概括。我们介绍了$ XB $的顶点加权版本，并显示此功能允许删除 - 触发关系。我们还证明，通过将$ xb $连接到其他图形函数，跨越树木的顶点加权$ XB $允许跨越TUTTE多项式的扩展。其次，我们提供了几种构造具有相等色和tutte对称函数的非构形图的方法，并使用它们来提供特定的示例。
This paper has two main parts. First, we consider the Tutte symmetric function $XB$, a generalization of the chromatic symmetric function. We introduce a vertex-weighted version of $XB$ and show that this function admits a deletion-contraction relation. We also demonstrate that the vertex-weighted $XB$ admits spanning-tree and spanning-forest expansions generalizing those of the Tutte polynomial by connecting $XB$ to other graph functions. Second, we give several methods for constructing nonisomorphic graphs with equal chromatic and Tutte symmetric functions, and use them to provide specific examples.
