Now showing items 1-20 of 43

    • A general method to obtain the spectrum and local spectra of a graph from its regular partitions 

      Dalfó, Cristina; Fiol, Miguel Angel (International Linear Algebra Society, 2020-07-12)
      It is well known that, in general, part of the spectrum of a graph can be obtained from the adjacency matrix of its quotient graph given by a regular partition. In this paper, a method that gives all the spectrum, and also ...
    • A new approach to gross error detection for GPS networks 

      Dalfó, Cristina; Fiol, Miguel Angel (Elsevier, 2019)
      We present a new matrix-based approach to detect and correct gross errors in GPS geodetic control networks. The study is carried out by introducing a new matrix, whose entries are powers of a (real or complex) variable, ...
    • A new general family of mixed graphs 

      Dalfó, Cristina (Elsevier, 2018)
      A new general family of mixed graphs is presented, which generalizes both the pancake graphs and the cycle prefix digraphs. The obtained graphs are vertex transitive and, for some values of the parameters, they constitute ...
    • A note on a new general family of deterministic hierarchical networks 

      Dalfó, Cristina; Fiol, Miguel Angel (World Scientific Publishing, 2019)
      It is known that many networks modeling real-life complex systems are small-word (large local clustering and small diameter) and scale-free (power law of the degree distribution), and very often they are also hierarchical. ...
    • A note on the order of iterated line digraphs 

      Dalfó, Cristina; Fiol, Miguel Angel (Wiley Periodicals Inc., 2016-06)
      Given a digraph G, we propose a new method to find therecurrence equation for the number of vertices nk of the k-iterated linedigraph Lk(G), for k≥0, where L0(G)=G. We obtain this result by usingthe minimal polynomial of ...
    • A survey on the missing Moore graph 

      Dalfó, Cristina (Elsevier, 2019-01-16)
      This is a survey on some known properties of the possible Moore graph (or graphs) ϒ with degree 57 and diameter 2. Moreover, we give some new results about it, such as the following. When we consider the distance partition ...
    • An algebraic approach to lifts of digraphs 

      Dalfó, Cristina; Fiol, Miguel Angel; Miller, Mirka; Ryan, Joe; Sirán, Jozef (Elsevier, 2018)
      We present some applications of a new matrix approach for studying the properties of the lift of a voltage digraph, which has arcs weighted by the elements of a group. As a main result, when the involved group is Abelian, ...
    • An improved Moore bound and some new optimal families of mixed Abelian Cayley graphs 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio; Ryan, Joe (Elsevier, 2020)
      We consider the case in which mixed graphs (with both directed and undirected edges) are Cayley graphs of Abelian groups. In this case, some Moore bounds were derived for the maximum number of vertices that such graphs can ...
    • An improved upper bound for the order of mixed graphs 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (Elsevier B.V., 2018)
      A mixed graph G can contain both (undirected) edges and arcs (directed edges). Here we derive an improved Moore-like bound for the maximum number of vertices of a mixed graph with diameter at least three. Moreover, a ...
    • Bipartite biregular Moore graphs 

      Araujo Pardo, Martha Gabriela; Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio (Elsevier, 2021)
      A bipartite graph G=(V,E) with V=V1 U V2 is biregular if all the vertices of a stable set Vi have the same degree ri for i=1,2. In this paper, we give an improved new Moore bound for an infinite family of such graphs with ...
    • Characterizing identifying codes from the spectrum of a graph or digraph 

      Balbuena Martínez, Camino; Dalfó, Cristina; Martínez Barona, Berenice (Elsevier, 2019)
      A (1, ≤ ℓ)-identifying code in digraph D is a dominating subset C of vertices of D, such that all distinct subsets of vertices of D with cardinality at most ℓ have distinct closed in-neighborhoods within C. As far as we ...
    • Cospectral digraphs from locally line digraphs 

      Dalfó, Cristina; Fiol, Miguel Angel (Elsevier, 2016-07)
      A digraph Γ =(V, E) is a line digraph when every pair of vertices u, v∈V have either equal or disjoint in-neighborhoods. When this condition only applies for vertices in a given subset (with at least two elements), we say ...
    • Decompositions of a rectangle into non-congruent rectangles of equal area 

      Dalfó, Cristina; Fiol, Miguel Angel; López Lorenzo, Ignacio; Martínez Pérez, Álvaro (Elsevier, 2021-06)
      In this paper, we deal with a simple geometric problem: Is it possible to partition a rectangle into k non-congruent rectangles of equal area? This problem is motivated by the so-called 'Mondrian art problem' that asks a ...
    • Deterministic hierarchical networks 

      Barrière, Lali; Comellas, Francesc; Dalfó, Cristina; Fiol, Miguel Angel (IOP Publishing, 2016-05)
      It has been shown that many networks associated with complex systems are small-world (they have both a large local clustering coefficient and a small diameter) and they are also scale-free (the degrees are distributed ...
    • Edge distance-regular graphs 

      Cámara Vallejo, Marc; Dalfó, Cristina; Fàbrega Canudas, José; Fiol, Miguel Angel; Garriga Valle, Ernest (Elsevier, 2011-12)
      Edge-distance-regularity is a concept recently introduced by the authors which is similar to that of distance-regularity, but now the graph is seen from each of its edges instead of from its vertices. More precisely, a ...
    • El mètode de les línies per a la resolució aproximada d'equacions en derivades parcials 

      Dalfó, Cristina; Fiol, Miguel Angel (Societat Catalana de Matemàtiques, Institut d’Estudis Catalans, 2019)
      En aquest treball es descriu un mètode numèric semidiscret per a la resolució d'un tipus d'equacions en derivades parcials. És conegut com el mètode de les línies (MOL, per les sigles en anglès), i es basa en la discretització ...
    • From expanded digraphs to lifts of voltage digraphs and line digraphs 

      Dalfó, Cristina; Fiol, Miguel Angel; Miller, Mirka; Ryan, Joe (Combinatorial Mathematics Society of Australasia (CMSA), 2017)
      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 between lifted digraphs of voltage digraphs ...
    • From Subkautz Digraphs to Cyclic Kautz Digraphs 

      Dalfó, Cristina (World Scientific Publishing, 2018)
      Kautz digraphs K(d, l) are a well-known family of dense digraphs, widely studied as a good model for interconnection networks. Closely related with these, the cyclic Kautz digraphs CK(d, l) were recently introduced by ...
    • Graphs, friends and acquaintances 

      Dalfó, Cristina; Fiol, Miguel Angel (Faculty of Mathematics and Natural Sciences; Institut Teknologi Bandung (ITB) Indonesia; Indonesian Combinatorial Society (InaCombS); GTA Research GroupGTA Research Group, 2018)
      A graph is a mathematical object modeling the existence of a certain relation between pairs of elements of a given set. Many of the first results concerning graphs made reference to relationships between groups of people. ...
    • Identifying codes in line digraphs 

      Balbuena Martínez, Camino; Dalfó, Cristina; Martínez Barona, Berenice (Elsevier, 2020-05-21)
      Given an integer ≥1, a (1, ≤ )-identifying code in a digraph is a dominating subset C of vertices such that all distinct subsets of vertices of cardinality at most have distinct closed in-neighborhoods within C . In ...