[HTML][HTML] Garland's method for token graphs

A Lew - Linear Algebra and its Applications, 2024 - Elsevier
The k-th token graph of a graph G=(V, E) is the graph F k (G) whose vertices are the k-
subsets of V and whose edges are all pairs of k-subsets A, B such that the symmetric …

[HTML][HTML] A general method to find the spectrum and eigenspaces of the k-token graph of a cycle, and 2-token through continuous fractions

MA Reyes, C Dalfó, MA Fiol, A Messegué - Discrete Applied Mathematics, 2025 - Elsevier
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 being adjacent whenever their symmetric difference is a pair of …

Spectral properties of token graphs

S Barik, P Verma - Linear Algebra and its Applications, 2024 - Elsevier
Let G be a graph on n vertices. For a given integer k such that 1≤ k≤ n, the k-token graph F
k (G) of G is defined as the graph whose vertices are the k-subsets of the vertex set of G, and …

Some bounds on the Laplacian eigenvalues of token graphs

C Dalfó, MÀ Fiol, A Messegué - arXiv preprint arXiv:2309.09041, 2023 - arxiv.org
The $ k $-token graph $ F_k (G) $ of a graph $ G $ on $ n $ vertices is the graph whose
vertices are the ${n\choose k} $$ k $-subsets of vertices from $ G $, two of which being …

On factored lifts of graphs and their spectra

C Dalfó, MA Fiol, S Pavlíková, J Sirán - arXiv preprint arXiv:2404.02128, 2024 - arxiv.org
arXiv:2404.02128v1 [math.CO] 2 Apr 2024 Page 1 On factored lifts of graphs and their spectra
∗ C. Dalfóa, MA Fiolb, S. Pavlıkovác, and J. Širánd aDepartament. de Matem`atica Universitat …

Combined voltage assignments, factored lifts, and their spectra

C Dalfó, MA Fiol, S Pavlíková, J Širáň - arXiv preprint arXiv:2409.02463, 2024 - arxiv.org
We consider lifting eigenvalues and eigenvectors of graphs to their {\em factored lifts},
derived by means of a {\em combined voltage assignment} in a group. The latter extends the …