论文标题
邻里多项式的注释
Notes on the Neighborhood Polynomials
论文作者
论文摘要
图$ g $的邻域多项式，用$ n（g，x）$表示，是$ g $的顶点子集数量的生成功能，这些函数是$ g $的开放式顶点的子集。对于任何图形多项式，通过引入一些限制和特征来生成新的多项式家族可能是有用的。在本文中，我们通过在顶点子集中添加独立性或连接性限制或通过$ n（g，x）$生成的顶点子集诱导的子图，从$ n（g，x）$获得的两个新图多项式。这些新的多项式不仅与$ n（g，x）$相关，而且与G或其子图的其他已知图多项式具有牢固的连接，例如独立多项式或子图组件多项式。
The neighborhood polynomial of graph $G$, denoted by $N(G,x)$, is the generating function for the number of vertex subsets of $G$ which are subsets of open neighborhoods of vertices in $G$. For any graph polynomial, it can be useful to generate a new family of polynomials by introducing some restrictions and characterizations. In this paper, we investigate two new graph polynomials that are obtained from $N(G,x)$ by adding independence or connectivity restrictions to the vertex subsets or to the subgraphs induced by the vertex subsets which are generated by $N(G,x)$. These new polynomials are not only related to $N(G,x)$, but also having strong connections to other known graph polynomials of G or its subgraphs, such as independence polynomials or subgraph component polynomials.
