10 citations · 20 across the 23 of their papers we have counts for
27 papers · 1 filter
On the Spectra of Generalized Token Graphs of Stars
Cristina Dalfó, Miquel Àngel Fiol, Berenice Martínez-Barona +1
In the generalization of token graphs (or supertoken graphs), the vertices of a -token graph of a graph correspond to distinguishable or indistinguishable tokens placed…
The Algebraic Connectivity and Laplacian Spectral Radius of Token Graphs
Xiaodi Song, Cristina Dalfó, Miquel Àngel Fiol +1
For a graph of order and an integer between and , its token graph is the graph whose vertices consist of the $\binom{n}{k}…
On supertoken graphs
Mónica A. Reyes, Cristina Dalfó, Miquel Àngel Fiol
We generalize the concept of token graphs to obtain supertoken graphs. In the latter case, there can be more than one token in a vertex. We formally define supertoken graphs and es…
On Generalized Token Graphs
Xiaodi Song, Cristina Dalfó, Miquel Àngel Fiol +2
The vertices of a -token graph of a graph correspond to indistinguishable tokens placed on different vertices of . Changing some conditions on both the nature of…
The Shannon capacity of graph powers
Aida Abiad, Cristina Dalfó, Miquel Àngel Fiol
For a graph , its -th graph power is constructed by placing an edge between two vertices if they are within distance . We consider the problem of deriving upper boun…
On bipartite biregular large graphs
G. Araujo-Pardo, C. Dalfó, M. A. Fiol +1
A bipartite graph with is biregular if all the vertices of each stable set, and , have the same degree, and , respectively. This paper s…
Token graphs of Cayley graphs as lifts
C. Dalfó, M. A. Fiol, S. Pavlíková +1
This paper describes a general method for representing -token graphs of Cayley graphs as lifts of voltage graphs. This allows us to construct line graphs of circulant graphs and…
Note on the product of the largest and the smallest eigenvalue of a graph
Aida Abiad, Cristina Dalfó, Miquel Àngel Fiol
In this note, we use eigenvalue interlacing to derive an inequality between the maximum degree of a graph and its maximum and minimum adjacency eigenvalues. The case of equality is…
On the spectra of token graphs of cycles and other graphs
Mónica. A. Reyes, Cristina Dalfó, Miquel Àngel Fiol +1
The -token graph of a graph is the graph whose vertices are the -subsets of vertices from , two of which being adjacent whenever their symmetric difference is…
On large regular (1,1,k)-mixed graphs
C. Dalfó, G. Erskine, G. Exoo +4
An -mixed graph has every vertex with undirected degree , directed in- and out-degree , and diameter . In this paper, we study the case , proposing som…
On the algebraic connectivity of token graphs
C. Dalfó, M. A. Fiol
We study the algebraic connectivity (or second Laplacian eigenvalue) of token graphs, also called symmetric powers of graphs. The -token graph of a graph is the gra…
On inertia and ratio type bounds for the -independence number of a graph and their relationship
Aida Abiad, Cristina Dalfó, Miquel Àngel Fiol +1
For , the -independence number of a graph is the maximum number of vertices that are mutually at distance greater than . The well-known inertia and ratio bounds…
On the Laplacian spectra of token graphs
C. Dalfó, F. Duque, R. Fabila-Monroy +4
We study the Laplacian spectrum of token graphs, also called symmetric powers of graphs. The -token graph of a graph is the graph whose vertices are the -subsets…
On symmetric association schemes and associated quotient-polynomial graphs
M. A. Fiol, Safet Penjić
Let denote an undirected, connected, regular graph with vertex set , adjacency matrix , and distinct eigenvalues. Let denote the su…
New results for the Mondrian art problem
C. Dalfó, M. A. Fiol, N. López
The Mondrian problem consists of dissecting a square of side length $n\in \NN$ into non-congruent rectangles with natural length sides such that the difference between the l…
A note on the spectra and eigenspaces of the universal adjacency matrices of arbitrary lifts of graphs
C. Dalfó, M. A. Fiol, S. Pavlíková +1
The universal adjacency matrix of a graph , with adjacency matrix , is a linear combination of , the diagonal matrix of vertex degrees, the identity matrix , an…
On -Fibonacci digraphs
C. Dalfó, M. A. Fiol
The -Fibonacci digraphs , introduced here, have the number of vertices following generalized Fibonacci-like sequences. They can be defined both as digraphs on alphabets…
New results on the degree/diameter problem of mixed Abelian Cayley graphs
C. Dalfó, M. A. Fiol, N. López
Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case in which such graphs are Cayley grap…
A new class of polynomials from to the spectrum of a graph, and its application to bound the -independence number
M. A. Fiol
The -independence number of a graph is the maximum size of a set of vertices at pairwise distance greater than . A graph is called -partially walk-regular if the number of…
On bipartite mixed graphs
C. Dalfó, M. A. Fiol, N. López
Mixed graphs can be seen as digraphs that have both arcs and edges (or digons, that is, two opposite arcs). In this paper, we consider the case where such graphs are bipartite. As…
The Dilating Method for Cayley digraphs on finite Abelian groups
F. Aguiló, M. A. Fiol, S. Pérez
A geometric method for obtaining an infinite family of Cayley digraphs of constant density on finite Abelian groups is presented. The method works for any given degree and it is ba…
From expanded digraphs to lifts of voltage digraphs and line digraphs
C. Dalfó, M. A. Fiol, M. Miller +1
In this note we present a general approach to construct large digraphs from small ones. These are called expanded digraphs, and, as particular cases, we show the close relationship…
Equivalent characterizations of the spectra of graphs and applications to measures of distance-regularity
V. Diego, J. Fàbrega, M. A. Fiol
As it is well known, the spectrum (of the adjacency matrix ) of a graph , with distinct eigenvalues other than its spectral radius , usually provides…
Quotient-polynomial graphs
M. A. Fiol
As a generalization of orbit-polynomial and distance-regular graphs, we introduce the concept of a quotient-polynomial graph. In these graphs every vertex induces the same regu…