关于树的令牌图的连通性

Discret. Math. Theor. Comput. Sci. Pub Date : 2020-04-30 DOI:10.46298/dmtcs.7538

Ruy Fabila Monroy, J. Leaños, A. L. Trujillo-Negrete

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引用次数: 5

摘要

设$k$和$n$为整数，使得$1\leq k \leq n-1$，设$G$为阶为$n$的简单图。$G$的$k$ -token图$F_k(G)$是其顶点是$V(G)$的$k$ -子集的图，其中两个顶点在$F_k(G)$中相邻，只要它们的对称差是$G$的一条边。本文证明了如果$G$是树，那么$F_k(G)$的连通性等于$F_k(G)$的最小度。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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On the Connectivity of Token Graphs of Trees

Let $k$ and $n$ be integers such that $1\leq k \leq n-1$, and let $G$ be a simple graph of order $n$. The $k$-token graph $F_k(G)$ of $G$ is the graph whose vertices are the $k$-subsets of $V(G)$, where two vertices are adjacent in $F_k(G)$ whenever their symmetric difference is an edge of $G$. In this paper we show that if $G$ is a tree, then the connectivity of $F_k(G)$ is equal to the minimum degree of $F_k(G)$.

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Discret. Math. Theor. Comput. Sci.

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