Next Article in Journal
Integrability of Riemann-Type Hydrodynamical Systems and Dubrovin’s Integrability Classification of Perturbed KdV-Type Equations
Next Article in Special Issue
k-Zero-Divisor and Ideal-Based k-Zero-Divisor Hypergraphs of Some Commutative Rings
Previous Article in Journal
Effects of a Targeted Exercise Program on Inter-Leg Asymmetries in Patients with Patellofemoral Pain
Previous Article in Special Issue
An Upper Bound Asymptotically Tight for the Connectivity of the Disjointness Graph of Segments in the Plane
Article

Hamiltonicity of Token Graphs of Some Join Graphs

1
Unidad Académica de Matemáticas, Universidad Autónoma de Zacatecas, Zacatecas 98066, Mexico
2
Departamento de Matemáticas, Cinvestav, Mexico City 07360, Mexico
*
Author to whom correspondence should be addressed.
Academic Editor: Alice Miller
Symmetry 2021, 13(6), 1076; https://doi.org/10.3390/sym13061076
Received: 17 May 2021 / Revised: 11 June 2021 / Accepted: 11 June 2021 / Published: 16 June 2021
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 1kn1. 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 AB, defined as (AB)(BA), 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<n2. View Full-Text
Keywords: token graphs; Hamiltonicity; fan graphs token graphs; Hamiltonicity; fan graphs
Show Figures

Figure 1

MDPI and ACS Style

Adame, L.E.; Rivera, L.M.; Trujillo-Negrete, A.L. Hamiltonicity of Token Graphs of Some Join Graphs. Symmetry 2021, 13, 1076. https://doi.org/10.3390/sym13061076

AMA Style

Adame LE, Rivera LM, Trujillo-Negrete AL. Hamiltonicity of Token Graphs of Some Join Graphs. Symmetry. 2021; 13(6):1076. https://doi.org/10.3390/sym13061076

Chicago/Turabian Style

Adame, Luis E., Luis M. Rivera, and Ana L. Trujillo-Negrete. 2021. "Hamiltonicity of Token Graphs of Some Join Graphs" Symmetry 13, no. 6: 1076. https://doi.org/10.3390/sym13061076

Find Other Styles
Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Access Map by Country/Region

1
Back to TopTop