The Edge-Connectivity of Token Graphs

Leaños, Jesús; Ndjatchi, Christophe

doi:10.1007/s00373-021-02301-0

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2021

2024

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Cited by 5 publications

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“…Fabila-Monroy et al [12] began a systematic study of some properties of G {k} such as connectivity, diameter, clique number, chromatic number and Hamiltonicity. This line of research has been continued by different authors, see, e.g., [13][14][15][16][17][18][19][20][21].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonicity of Token Graphs of Some Join Graphs

2021

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Let G be a simple graph of order n with vertex set V(G) and edge set E(G), and let k be an integer such that 1≤k≤n−1. The k-token graph G{k} of G is the graph whose vertices are the k-subsets of V(G), where two vertices A and B are adjacent in G{k} whenever their symmetric difference A▵B, defined as (A∖B)∪(B∖A), is a pair {a,b} of adjacent vertices in G. In this paper we study the Hamiltonicity of the k-token graphs of some join graphs. We provide an infinite family of graphs, containing Hamiltonian and non-Hamiltonian graphs, for which their k-token graphs are Hamiltonian. Our result provides, to our knowledge, the first family of non-Hamiltonian graphs for which it is proven the Hamiltonicity of their k-token graphs, for any 2<k<n−2.

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