Now showing items 1-20 of 118

    • A Boolean algebra approach to the construction of snarks 

      Fiol Mora, Miquel Àngel (John Wiley & Sons, 1991)
      Part of book or chapter of book
      Open Access
      This work deals with the construction of snarks, that is, cubic graphs that cannot be 3-edge-colored. A natural generalization of the concept of "color", that describes in a simple way the coloring ("0" or "1") of any set ...
    • A differential approach for bounding the index of graphs under perturbations 

      Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (2011-09-02)
      Article
      Open Access
      This paper presents bounds for the variation of the spectral radius (G) of a graph G after some perturbations or local vertex/edge modifications of G. The perturbations considered here are the connection of a new vertex ...
    • A differential approach for bounding the index of graphs under perturbations 

      Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Garriga Valle, Ernest (2011-03)
      External research report
      Open Access
    • A discrete optimization problem in local networks and data alignment 

      Fiol Mora, Miquel Àngel; Andrés Yebra, José Luis; Alegre de Miguel, Ignacio; Valero Cortés, Mateo (1987-06)
      Article
      Restricted access - publisher's policy
      This paper presents the solution of the following optimization problem that appears in the design of double-loop structures for local networks and also in data memory, allocation and data alignment in SIMD processors. Consider ...
    • A geometric approach to dense Cayley digraphs of finite Abelian groups 

      Aguiló Gost, Francisco de Asis L.; Fiol Mora, Miquel Àngel; Pérez Mansilla, Sonia (Elsevier, 2016)
      Conference report
      Open Access
      We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related {\em minimum distance ...
    • A geometric approach to dense Cayley digraphs of finite Abelian groups 

      Aguiló Gost, Francisco de Asis L.; Fiol Mora, Miquel Àngel; Pérez Mansilla, Sonia (2016)
      Article
      Open Access
      We give a method for constructing infinite families of dense (or eventually likely dense) Cayley digraphs of finite Abelian groups. The diameter of the digraphs is obtained by means of the related minimum distance diagrams. ...
    • A mathematical model for dynamic memory networks 

      Fàbrega Canudas, José; Fiol Mora, Miquel Àngel; Serra Albó, Oriol; Andrés Yebra, José Luis (Iniciativa Digital Politècnica, 2011)
      Conference report
      Open Access
      The aim of this paper is to bring together the work done several years ago by M.A. Fiol and the other authors to formulate a quite general mathematical model for a kind of permutation networks known as dynamic memories. A ...
    • A new approach to gross error detection for GPS networks 

      Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel (2019-05-29)
      Article
      Open Access
      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 approach to the spectral excess theorem for distance-regular graphs 

      Fiol Mora, Miquel Àngel; Gago Álvarez, Silvia; Garriga Valle, Ernest (2009-04-01)
      Article
      Open Access
      The Spectral Excess Theorem provides a quasi-spectral characterization for a (regular) graph $\Gamma$ with $d+1$ different eigenvalues to be distance-regular graph, in terms of the mean (d-1)-excess of its vertices.\ The ...
    • A note on a new general family of deterministic hierarchical networks 

      Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel (2019-06-01)
      Article
      Open Access
      Hierarchical network; Small-word; Scale-free; Routing algorithm; Diameter; Clustering
    • A note on the order of iterated line digraphs 

      Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel (Wiley, 2016-07-27)
      Article
      Open Access
      Given a digraph G, we propose a new method to find the recurrence equation for the number of vertices n_k of the k-iterated line digraph L_k(G), for k>= 0, where L_0(G) = G. We obtain this result by using the minimal polynomial ...
    • A simple proof of the spectral excess theorem for distance-regular graphs 

      Fiol Mora, Miquel Àngel; Gago Álvarez, Silvia; Garriga Valle, Ernest (Elsevier, 2010-04-15)
      Article
      Restricted access - publisher's policy
      The spectral excess theorem provides a quasi-spectral characterization for a (regular) graph Γ with d+1 distinct eigenvalues to be distance-regular graph, in terms of the excess (number of vertices at distance d) of each ...
    • Abelian Cayley digraphs with asymptotically large order for any given degree 

      Aguiló Gost, Francisco de Asis L.; Fiol Mora, Miquel Àngel; Pérez Mansilla, Sonia (2016-04-29)
      Article
      Open Access
      Abelian Cayley digraphs can be constructed by using a generalization to Z(n) of the concept of congruence in Z. Here we use this approach to present a family of such digraphs, which, for every fixed value of the degree, ...
    • Algebraic characterizations of bipartite distance-regular graphs 

      Fiol Mora, Miquel Àngel (Iniciativa Digital Politècnica, 2011)
      Conference report
      Open Access
      Bipartite graphs are combinatorial objects bearing some interesting symmetries. Thus, their spectra—eigenvalues of its adjacency matrix—are symmetric about zero, as the corresponding eigenvectors come into pairs. Moreover, ...
    • Algebraic characterizations of distance-regular graphs 

      Fiol Mora, Miquel Àngel (Elsevier, 2002)
      Article
      Open Access
      We survey some old and some new characterizations of distance-regular graphs, which depend on information retrieved from their adjacency matrix. In particular, it is shown that a regular graph with d+1 distinct eigenvalues ...
    • Algebraic Characterizations of Regularity Properties in Bipartite Graphs 

      Abiad Monge, Aida; Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel (2013)
      Article
      Restricted access - publisher's policy
      Regular and distance-regular characterizations of general graphs are well-known. In particular, the spectral excess theorem states that a connected graph GG is distance-regular if and only if its spectral excess (a number ...
    • Algunos grafos compuestos 

      Fiol Mora, Miquel Àngel; Fàbrega Canudas, José (Universidad de Barcelona, Departamento de Estadística Matemática;Universidad Politécnica de Barcelona, Escuela Técnica Superior de Arquitectura, Departamento de Matemáticas y Estadística, 1983)
      Article
      Open Access
      From two graphs $G_1$ and $G_2$ on $N_1$ and $N_2$ vertices respectively, the compound graph $G_1[G_2]$ on $N_1N_2$ vertices is obtained connecting $N_2$ copies of $G_1$ following the structure of $G_2$. We present in ...
    • An algebraic approach to lifts of digraphs 

      Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Miller, Mirka; Ryan, Joe; Siran, Josef (2019-09-30)
      Article
      Restricted access - publisher's policy
      We study the relationship between two key concepts in the theory of (di)graphs: the quotient digraph, and the lift Ga of a base (voltage) digraph. These techniques contract or expand a given digraph in order to study its ...
    • An algebraic model for the storage of data in parallel memories 

      Fiol Mora, Miquel Àngel; Serra Albó, Oriol (Springer, 1989)
      Part of book or chapter of book
      Open Access
      The use of SIMD computers requires efficient schemes of storage of data in order to have conflict-free acces in parallel computation. In this paper we restate the problem of finding such chemes in an algebraic context. ...
    • An eigenvalue characterization of antipodal distance-regular graphs 

      Fiol Mora, Miquel Àngel (1997-11)
      Article
      Open Access
      Let $\Gamma$ be a regular (connected) graph with $n$ vertices and $d+1$ distinct eigenvalues. As a main result, it is shown that $\Gamma$ is an $r$-antipodal distance-regular graph if and only if the distance graph $\Gamma_d$ ...