Hamiltonicity of token graphs of fan graphs

Rivera, Luis Manuel; Trujillo-Negrete, Ana Laura

doi:10.26493/2590-9770.1244.720

Cited by 14 publications

(14 citation statements)

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“…In 2018, Rivera and Trujillo-Negrete [28] showed the Hamiltonicity of F {k} 1,n , for any integers k and n with 1 < k < n. In this paper, we study the Hamiltonicity of the k-token graphs of fan graphs F m,n , for m > 1. The family of fan graphs F m,n contains an infinite number of graphs containing no Hamiltonian paths, precisely, when m > n + 1.…”

Section: Basic Definitions and Resultsmentioning

confidence: 97%

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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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Section: Basic Definitions and Resultsmentioning

confidence: 97%

“…The Hamiltonicity of F {k} 1,n was proved in [28]. However, in order to prove Theorem 2 we need a special Hamiltonian cycle in F For i with k − 1 ≤ i ≤ n, let H i be the subgraph of F {k} 1,n induced by the vertex set…”

Section: Proof Of Theoremmentioning

confidence: 99%

Hamiltonicity of Token Graphs of Some Join Graphs

2021

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“…The authors of this article studied the Hamiltonicity of k-token graphs of fan graphs F 1,n [16]. In this note, we continue with this line of research but for the case of the complete double vertex graph of the generalized fan graphs F m,n , for m ≥ 1.…”

Section: Introductionmentioning

confidence: 93%

Hamiltonicity of the Complete Double Vertex Graph of some Join Graphs

Rivera¹,

Trujillo-Negrete

2022

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“…The authors of this article studied the Hamiltonicity of k-token graphs of fan graphs F 1,n [17]. In this note, we continue with this line of research but for the case of the complete double vertex graph of the generalized fan graphs F m,n , for m ≥ 1.…”

Section: Introductionmentioning

confidence: 93%