On the algebraic connectivity of some token graphs

The k -token graph F k ( G ) 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 F k ( G ) equals the algebraic connectivi...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Journal of algebraic combinatorics Jg. 60; H. 1; S. 45 - 56
Hauptverfasser: Dalfó, C., Fiol, M. A.
Format: Journal Article
Sprache:Englisch
Veröffentlicht: New York Springer US 01.08.2024
Springer Nature B.V
Schlagworte:
Algebra
Apexes
Combinatorial analysis
Combinatorics
Computer Science
Connectivity
Convex and Discrete Geometry
Eigenvalues
Eigenvectors
Graph theory
Graphs
Group Theory and Generalizations
Lattices
Mathematics
Mathematics and Statistics
Order
Ordered Algebraic Structures
Random walk
Trees (mathematics)
05C10
05C50
Laplacian spectrum
Algebraic connectivity
Token graph
Binomial matrix
05C15
ISSN:0925-9899, 1572-9192
Online-Zugang:Volltext
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Beschreibung
Zusammenfassung:The k -token graph F k ( G ) 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 F k ( G ) 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 F k ( G ) 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.
Bibliographie:ObjectType-Article-1
SourceType-Scholarly Journals-1
ObjectType-Feature-2
content type line 14
ISSN:0925-9899
1572-9192
DOI:10.1007/s10801-024-01323-0