On the algebraic connectivity of some token graphs
The k-token graph of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It was proved that the algebraic connectivity of equals the algebraic connectivity of G with a proof usi...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2024 |
| País: | España |
| Institución: | Universitat Politècnica de Catalunya (UPC) |
| Repositorio: | UPCommons. Portal del coneixement obert de la UPC |
| Idioma: | inglés |
| OAI Identifier: | oai:upcommons.upc.edu:2117/419718 |
| Acceso en línea: | https://hdl.handle.net/2117/419718 https://dx.doi.org/10.1007/s10801-024-01323-0 |
| Access Level: | acceso abierto |
| Palabra clave: | Graph theory Token graph Laplacian spectrum Algebraic connectivity Binomial matrix Grafs, Teoria de Classificació AMS::05 Combinatorics::05C Graph theory Àrees temàtiques de la UPC::Matemàtiques i estadística::Matemàtica discreta::Teoria de grafs |
| Sumario: | The k-token graph of a graph G is the graph whose vertices are the k-subsets of vertices from G, two of which are adjacent whenever their symmetric difference is a pair of adjacent vertices in G. It was proved that the algebraic connectivity of equals the algebraic connectivity of G with a proof using random walks and interchange of processes on a weighted graph. However, no algebraic or combinatorial proof is known, and it would be a hit in the area. In this paper, we algebraically prove that the algebraic connectivity of equals the one of G for new infinite families of graphs, such as trees, some graphs with hanging trees, and graphs with minimum degree large enough. Some examples of these families are the following: the cocktail party graph, the complement graph of a cycle, and the complete multipartite graph. |
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