The automorphisms of 2-token graphs

Zhang, Ju; Zhou, Jin‐Xin; Li, Yantao; Kwon, Young Soo

doi:10.1016/j.amc.2023.127872

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2023

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Cited by 2 publications

(2 citation statements)

References 14 publications

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“…1 Upon finishing this preprint we learned that Theorems 3 and 4 have recently been proved in [ZZLK23].…”

Section: It Is Known Thatmentioning

confidence: 99%

On the Connectivity of Token Graphs of Trees

Fabila-Monroy¹,

Leaños²,

Trujillo-Negrete³

2022

Discrete Mathematics &Amp; Theoretical Computer Science

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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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“…1 Upon finishing this preprint we learned that Theorems 3 and 4 have recently been proved in [ZZLK23].…”

Section: It Is Known Thatmentioning

confidence: 99%

On the Connectivity of Token Graphs of Trees

Fabila-Monroy¹,

Leaños²,

Trujillo-Negrete³

2022

Discrete Mathematics &Amp; Theoretical Computer Science

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“…In reference [12], automorphism groups of fundamental groups of graphs of groups in which the edge groups are incomparable up to conjugacy are presented. Automorphism groups for particular token graphs are given in [10] and particularly for the 2-token graphs,the automorphism groups are given in [17].…”

Section: Introductionmentioning

confidence: 99%

On the 2-Token Graphs of Some Disjoint Union of Graphs

Susanti,

2023

MJMS

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The k-token graph of a given graph G, is the graph which vertex set consists of all k− subsets of the vertex set of G and two vertices are connected by an edge exactly when their difference corresponds to an edge of G. In this paper, we give a description on the structure of the 2-token graph of disjoint union of multiple graphs. This result complements the previous findings regarding the properties of the k-token graphs.

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The automorphisms of 2-token graphs

Cited by 2 publications

References 14 publications

On the Connectivity of Token Graphs of Trees

On the Connectivity of Token Graphs of Trees

On the 2-Token Graphs of Some Disjoint Union of Graphs

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