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- Title
Hamiltonicity of Token Graphs of Some Join Graphs.
- Authors
Adame, Luis Enrique; Rivera, Luis Manuel; Trujillo-Negrete, Ana Laura
- Abstract
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 .
- Subjects
HAMILTONIAN graph theory; LINEAR orderings; INTEGERS
- Publication
Symmetry (20738994), 2021, Vol 13, Issue 6, p1076
- ISSN
2073-8994
- Publication type
Article
- DOI
10.3390/sym13061076