图的二分多项式：重构、分解及应用
The Bipartition Polynomial of a Graph: Reconstruction, Decomposition, and Applications
摘要：
图的二分多项式是许多其他图多项式的推广，包括控制多项式、伊辛多项式、匹配多项式、独立多项式、割多项式和欧拉多项式。我们在本文中表明，它也是一个强大的工具，证明图形的性质。此外，我们还证明了二划分多项式是多项式可重构的，这意味着我们可以从单边消去子图的二划分多项式的多个集合中恢复它。
英文摘要：
The bipartition polynomial of a graph is a generalization of many other graph polynomials, including the domination, Ising, matching, independence, cut, and Euler polynomial. We show in this paper that it is also a powerful tool for proving graph properties. In addition, we can show that the bipartition polynomial is polynomially reconstructible, which means that we can recover it from the multiset of bipartition polynomials of one-edge-deleted subgraphs.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
