论文标题
关于通过其准对称B-多项式区分挖掘图
On distinguishing digraphs by its quasisymmetric B-polynomial
论文作者
论文摘要
J. Awan和O. Bernardi定义的$ B $ - 多项式元素是Tutte多项式对Digraphs的概括。在本文中，我们解决了J. Awan和O. Bernardi提出的一个关于$ b $ $ $ polynomial在基本对称多项式中的扩展的公开问题。我们表明，$ b $ - 多项式的准对称概括区分了一类定向的适当毛毛虫和方向的路径。我们提出了涉及删除源或水槽的准对称$ b $ b $多物种的复发关系。 As a consequence, we prove that a class of digraph $\mathcal{D}$ is distinguishable if and only if the class $\mathcal{D}^{\vee}$ obtained by taking directed join of $K_1$ with each digraph in $\mathcal{D}$ is distinguishable, which concludes that the digraph analogue of Stanley's Tree conjecture holds for a大型的无环挖掘。我们进一步研究了准对称$ b $ polynomial的对称特性及其与某些图形的关系。
The $B$-polynomial defined by J. Awan and O. Bernardi is a generalization of Tutte Polynomial to digraphs. In this paper, we solve an open question raised by J. Awan and O. Bernardi regarding the expansion of $B$-polynomial in elementary symmetric polynomials. We show that the quasisymmetric generalization of the $B$-polynomial distinguishes a class of oriented proper caterpillars and the class of oriented paths. We present a recurrence relation for the quasisymmetric $B$-polynomial involving the deletion of a source or a sink. As a consequence, we prove that a class of digraph $\mathcal{D}$ is distinguishable if and only if the class $\mathcal{D}^{\vee}$ obtained by taking directed join of $K_1$ with each digraph in $\mathcal{D}$ is distinguishable, which concludes that the digraph analogue of Stanley's Tree conjecture holds for a large class of acyclic digraphs. We further study the symmetric properties of the quasisymmetric $B$-polynomial and its relation with certain digraphs.
