24 research outputs found
Certain particular families of graphicable algebras
In this paper, we introduce some particular families of graphicable
algebras obtained by following a relatively new line of research, initiated
previously by some of the authors. It consists of the use of certain objects of Discrete Mathematics, mainly graphs and digraphs, to facilitate the study of graphicable algebras, which are a subset of evolution algebras
Note on power hypergraphs with equal domination and matching numbers
We present some examples that refute two recent results in the literature
concerning the equality of the domination and matching numbers for power and
generalized power hypergraphs. In this note we pinpoint the flaws in the proofs
and suggest how they may be mended.Comment: 7 pages, 1 figure, XIII Encuentro Andaluz de Matem\'atica Discreta,
(C\'adiz) Spain, july, 202
Irreducible triangulations of the Möbius band
A complete list of irreducible triangulations is identified on the Möbius band.Plan Andaluz de Investigación (Junta de AndalucÃa)Ministerio de Ciencia e Innovació
Generating punctured surface triangulations with degree at least 4
As a sequel of a previous paper by the authors, we present here
a generating theorem for the family of triangulations of an arbitrary
punctured surface with vertex degree ≥ 4. The method is based on a
series of reversible operations termed reductions which lead to a minimal
set of triangulations in such a way that all intermediate triangulations
throughout the reduction process remain within the family. Besides contractible edges and octahedra, the reduction operations act on two new
configurations near the surface boundary named quasi-octahedra and
N-components. It is also observed that another configuration called
M-component remains unaltered under any sequence of reduction operations. We show that one gets rid of M-components by flipping appropriate edges
Irreducible triangulations of the once-punctured torus
A triangulation of a surface with fixed topological type is called irreducible if no edge can be contracted to a vertex while remaining in the category of simplicial complexes and preserving the topology of the surface. A complete list of combinatorial structures of irreducible triangulations is made by hand for the once-punctured torus, consisting of exactly 297 non-isomorphic triangulations.Plan Andaluz de Investigación (Junta de AndalucÃa)Ministerio de Ciencia e Innovació
Classification of filiform Lie algebras up to dimension 7 over finite fields
This paper tries to develop a recent research which consists in using
Discrete Mathematics as a tool in the study of the problem of the
classification of Lie algebras in general, dealing in this case with filiform
Lie algebras up to dimension 7 over finite fields. The idea lies in the
representation of each Lie algebra by a certain type of graphs. Then, some properties on Graph Theory make easier to classify the algebras. As main results, we find out that there exist, up to isomorphism, six, five and five 6-dimensional filiform Lie algebras and fifteen, eleven and fifteen 7-dimensional ones, respectively, over Z/pZ, for p = 2, 3, 5. In any case, the main interest of the paper is not the computations itself but both to provide new strategies to find out properties of Lie algebras and to exemplify a suitable technique to be used in classifications for larger dimensions
Computation of isotopisms of algebras over finite fields by means of graph invariants
In this paper we define a pair of faithful functors that map isomorphic and
isotopic finite-dimensional algebras over finite fields to isomorphic graphs.
These functors reduce the cost of computation that is usually required
to determine whether two algebras are isomorphic. In order to illustrate
their efficiency, we determine explicitly the classification of two- and threedimensional partial quasigroup rings
K-Factores en nubes bicromáticas
Consideramos una colección de puntos bicromática y nos preguntamos cuántos puntos adicionales son necesarios considerar para asegurar la existencia de un k {factor. Dos tipos de puntos adicionales serán tratados: puntos de Steiner y puntos blancos (con posición prefijada pero no asÃ
su color