On the 2-token graph of a graph

Deepalakshmi, J.; Marimuthu, G.; Somasundaram, A.; Arumugam, S.

doi:10.1016/j.akcej.2019.05.002

Cited by 11 publications

(10 citation statements)

References 2 publications

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“…Jiménez-Sepúlveda and Rivera [15] determine α(T 2 (G)) when G is the fan graph and the wheel graph. A sharp lower bound on α(T 2 (G)) appears in work of Deepalakshmi, Marimuthu, Somasundaram, and Arumugam [9] (also see Remark 3.5).…”

Section: Introductionmentioning

confidence: 93%

Well-covered token graphs

Abdelmalek¹,

Tuyl²,

Meulen³

et al. 2023

Discuss. Math. Graph Theory

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The k-token graph T k (G) is the graph whose vertices are the k-subsets of vertices of a graph G, with two vertices of T k (G) adjacent if their symmetric difference is an edge of G. We explore when T k (G) is a well-covered graph, that is, when all of its maximal independent sets have the same cardinality. For bipartite graphs G, we classify when T k (G) is well-covered. For an arbitrary graph G, we show that if T 2 (G) is well-covered, then the girth of G is at most four. We include upper and lower bounds on the independence number of T k (G), and provide some families of well-covered token graphs.

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Section: Introductionmentioning

confidence: 93%

Well-covered token graphs

Abdelmalek¹,

Tuyl²,

Meulen³

et al. 2023

Discuss. Math. Graph Theory

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“…The properties of token graphs have been studied since 1991 by various authors and with different names, see, e.g., [1,2,3,5,9] and, in recent years, the study of its combinatorial properties and its connection with problems in other areas such as Coding Theory and Physics has increased, see, e.g., [4,6,8,10,11,12,14,15]. However, there are only few papers about complete double vertex graphs, which were implicitly introduced by Chartrand et al [7].…”

Section: Introductionmentioning

confidence: 99%

Hamiltonicity of the Complete Double Vertex Graph of some Join Graphs

Rivera¹,

Trujillo-Negrete

2022

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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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On the 2-token graph of a graph

Cited by 11 publications

References 2 publications

Well-covered token graphs

Well-covered token graphs

Hamiltonicity of the Complete Double Vertex Graph of some Join Graphs

Hamiltonicity of Token Graphs of Some Join Graphs

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