论文标题
在代币图的代数连接上
On the algebraic connectivity of token graphs
论文作者
论文摘要
我们研究令牌图的代数连通性（或第二个拉普拉斯特征值），也称为图形的对称能力。图$ g $的$ k $ token Graph $ f_k（g）$是其顶点是$ g $的$ k $ - subset，其中两个是在$ g $中的两对相邻顶点时，其中两个是相邻的。最近，有人推测$ f_k（g）$的代数连接等于$ g $的代数连接。在本文中，我们证明了新的无限图族的猜想，例如树木和图形，最大程度足够大。
We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The $k$-token graph $F_k(G)$ of a graph $G$ is the graph whose vertices are the $k$-subsets of vertices from $G$, two of which being adjacent whenever their symmetric difference is a pair of adjacent vertices in $G$. Recently, it was conjectured that the algebraic connectivity of $F_k(G)$ equals the algebraic connectivity of $G$. In this paper, we prove the conjecture for new infinite families of graphs, such as trees and graphs with maximum degree large enough.
