论文标题
星集和相关图参数的主要顶点
The main vertices of a star set and related graph parameters
论文作者
论文摘要
V（g）$中的顶点$ v \如果属于$ X \ subset v（g）$ X \ subset V（g）$ g $ g $ g $的$ X \ subset v（g）$，则此eigenvalue是从$ g $获得$ g $通过$ x \ x setminus \ c \ g $ g $主要的，而该特征是最主要的，则称为$λ$ -Main。否则，$ v $是$λ$ -Non-Main。推导了有关特征值的主要和非主要顶点的一些结果。对于图$ g $的主要特征值$λ$，我们将$λ$ -Star套件的最低和最大数量$λ$ -Main顶点作为新的图形不变参数。这些参数的确定是基于单纯形方法的组合优化问题。使用这些和一些相关参数，我们开发了可用于同构问题研究中的新光谱工具。提供了$λ$ - main顶点的最大数量与$λ$ -Star集合的基数相吻合的图形示例。
A vertex $v \in V(G)$ is called $λ$-main if it belongs to a star set $X \subset V(G)$ of the eigenvalue $λ$ of a graph $G$ and this eigenvalue is main for the graph obtained from $G$ by deleting all the vertices in $X \setminus \{v\}$; otherwise, $v$ is $λ$-non-main. Some results concerning main and non-main vertices of an eigenvalue are deduced. For a main eigenvalue $λ$ of a graph $G$, we introduce the minimum and maximum number of $λ$-main vertices in some $λ$-star set of $G$ as new graph invariant parameters. The determination of these parameters is formulated as a combinatorial optimization problem based on a simplex-like approach. Using these and some related parameters we develop new spectral tools that can be used in the research of the isomorphism problem. Examples of graphs for which the maximum number of $λ$-main vertices coincides with the cardinality of a $λ$-star set are provided.
