COMBGRAF - Combinatòria, Teoria de Grafs i Aplicacions
http://hdl.handle.net/2117/3178
Mon, 30 May 2016 01:21:50 GMT2016-05-30T01:21:50ZOn the Partition Dimension and the Twin Number of a Graph
http://hdl.handle.net/2117/87267
On the Partition Dimension and the Twin Number of a Graph
Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel
A partition of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of . The partition dimension of G is the minimum cardinality of a locating partition of G . A pair of vertices u;v of a graph G are called twins if they have exactly the same set of neighbors other than u and v . A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a twin class of G . In this paper we undertake the study of the partition dimension of a graph by also considering its twin number. This approach allows us to obtain the set of connected graphs of order n 9 having partition dimension n
Tue, 24 May 2016 10:33:18 GMThttp://hdl.handle.net/2117/872672016-05-24T10:33:18ZHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelA partition of the vertex set of a connected graph G is a locating partition of G if every vertex is uniquely determined by its vector of distances to the elements of . The partition dimension of G is the minimum cardinality of a locating partition of G . A pair of vertices u;v of a graph G are called twins if they have exactly the same set of neighbors other than u and v . A twin class is a maximal set of pairwise twin vertices. The twin number of a graph G is the maximum cardinality of a twin class of G . In this paper we undertake the study of the partition dimension of a graph by also considering its twin number. This approach allows us to obtain the set of connected graphs of order n 9 having partition dimension nPerfect and quasiperfect domination in trees
http://hdl.handle.net/2117/86561
Perfect and quasiperfect domination in trees
Cáceres, José; Hernando Martín, María del Carmen; Mora Giné, Mercè; Pelayo Melero, Ignacio Manuel; Puertas, Maria Luz
A k quasip erfect dominating set of a connected graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k-quasip erfect dominating set in G is denoted by 1 k ( G ) . These graph parameters were rst intro duced by Chellali et al. (2013) as a generalization of b oth the p erfect domination numb er 11 ( G ) and the domination numb er ( G ) . The study of the so-called quasip erfect domination chain 11 ( G ) 12 ( G ) 1 ( G ) = ( G ) enable us to analyze how far minimum dominating sets are from b eing p erfect. In this pap er, we provide, for any tree T and any p ositive integer k , a tight upp er b ound of 1 k ( T ) . We also prove that there are trees satisfying all p ossible equalities and inequalities in this chain. Finally a linear algorithm for computing 1 k ( T ) in any tree T is presente
Wed, 04 May 2016 10:50:08 GMThttp://hdl.handle.net/2117/865612016-05-04T10:50:08ZCáceres, JoséHernando Martín, María del CarmenMora Giné, MercèPelayo Melero, Ignacio ManuelPuertas, Maria LuzA k quasip erfect dominating set of a connected graph G is a vertex subset S such that every vertex not in S is adjacent to at least one and at most k vertices in S . The cardinality of a minimum k-quasip erfect dominating set in G is denoted by 1 k ( G ) . These graph parameters were rst intro duced by Chellali et al. (2013) as a generalization of b oth the p erfect domination numb er 11 ( G ) and the domination numb er ( G ) . The study of the so-called quasip erfect domination chain 11 ( G ) 12 ( G ) 1 ( G ) = ( G ) enable us to analyze how far minimum dominating sets are from b eing p erfect. In this pap er, we provide, for any tree T and any p ositive integer k , a tight upp er b ound of 1 k ( T ) . We also prove that there are trees satisfying all p ossible equalities and inequalities in this chain. Finally a linear algorithm for computing 1 k ( T ) in any tree T is presenteCounting configuration–free sets in groups
http://hdl.handle.net/2117/86058
Counting configuration–free sets in groups
Rué Perna, Juan José; Serra Albó, Oriol; Vena Cros, Lluís
We present a unified framework to asymptotically count the number of sets, with a given cardinality, free of certain configurations. This is done by combining the hypergraph containers methodology joint with arithmetic removal lemmas. Several applications involving linear configurations are described, as well as some applications in the random sparse setting.
Thu, 21 Apr 2016 11:49:48 GMThttp://hdl.handle.net/2117/860582016-04-21T11:49:48ZRué Perna, Juan JoséSerra Albó, OriolVena Cros, LluísWe present a unified framework to asymptotically count the number of sets, with a given cardinality, free of certain configurations. This is done by combining the hypergraph containers methodology joint with arithmetic removal lemmas. Several applications involving linear configurations are described, as well as some applications in the random sparse setting.On sets of vectors of a finite vector space in which every subset of basis size is a basis II
http://hdl.handle.net/2117/85944
On sets of vectors of a finite vector space in which every subset of basis size is a basis II
Ball, Simeon Michael; De Beule, Jan
This article contains a proof of the MDS conjecture for k = 2p - 2. That is, that if S is a set of vectors of F k q in which every subset of S of size k is a basis, where q = p h, p is prime and q is not and k = 2p - 2, then |S| = q + 1. It also contains a short proof of the same fact for k = p, for all q.
The final publication is available at Springer via http://dx.doi.org/10.1007/s10623-012-9658-6
Wed, 20 Apr 2016 09:53:44 GMThttp://hdl.handle.net/2117/859442016-04-20T09:53:44ZBall, Simeon MichaelDe Beule, JanThis article contains a proof of the MDS conjecture for k = 2p - 2. That is, that if S is a set of vectors of F k q in which every subset of S of size k is a basis, where q = p h, p is prime and q is not and k = 2p - 2, then |S| = q + 1. It also contains a short proof of the same fact for k = p, for all q.Langford sequences and a product of digraphs
http://hdl.handle.net/2117/85652
Langford sequences and a product of digraphs
López Masip, Susana Clara; Muntaner Batle, Francesc Antoni
Skolem and Langford sequences and their many generalizations have applications in numerous areas. The ¿h-product is a generalization of the direct product of digraphs. In this paper we use the ¿h-product and super edge-magic digraphs to construct an exponential number of Langford sequences with certain order and defect. We also apply this procedure to extended Skolem sequences.
Thu, 14 Apr 2016 10:28:27 GMThttp://hdl.handle.net/2117/856522016-04-14T10:28:27ZLópez Masip, Susana ClaraMuntaner Batle, Francesc AntoniSkolem and Langford sequences and their many generalizations have applications in numerous areas. The ¿h-product is a generalization of the direct product of digraphs. In this paper we use the ¿h-product and super edge-magic digraphs to construct an exponential number of Langford sequences with certain order and defect. We also apply this procedure to extended Skolem sequences.Conjugacy in houghton's groups
http://hdl.handle.net/2117/85601
Conjugacy in houghton's groups
Antolin, Yago; Burillo Puig, José; Martino, Armando
Let n ∈ N. Houghton’s group Hn is the group of permutations of {1, . . . , n} × N, that eventually act as a translation in each copy of N. We prove the solvability of the conjugacy problem and conjugator search problem for Hn, n ≥ 2
Wed, 13 Apr 2016 11:34:32 GMThttp://hdl.handle.net/2117/856012016-04-13T11:34:32ZAntolin, YagoBurillo Puig, JoséMartino, ArmandoLet n ∈ N. Houghton’s group Hn is the group of permutations of {1, . . . , n} × N, that eventually act as a translation in each copy of N. We prove the solvability of the conjugacy problem and conjugator search problem for Hn, n ≥ 2Lissajous curves: an experiment in creative coding
http://hdl.handle.net/2117/85586
Lissajous curves: an experiment in creative coding
Barrière Figueroa, Eulalia
Do you want to become a creative coder for a day? When artists use a computer to make art, they often experience the need of improving their mathematical skills. On the other hand, students with technical skills are less comfortable with aesthetic issues and creative work. In this workshop we use Processing to build two animations that involve: (1) the use of trigonometry and polar coordinates in parametric curves, and (2) the (soft) implementation of Hooke’s law. Our goal is to show that creative coding is a rewarding way of learning mathematics, with a creative approach.
Wed, 13 Apr 2016 09:45:14 GMThttp://hdl.handle.net/2117/855862016-04-13T09:45:14ZBarrière Figueroa, EulaliaDo you want to become a creative coder for a day? When artists use a computer to make art, they often experience the need of improving their mathematical skills. On the other hand, students with technical skills are less comfortable with aesthetic issues and creative work. In this workshop we use Processing to build two animations that involve: (1) the use of trigonometry and polar coordinates in parametric curves, and (2) the (soft) implementation of Hooke’s law. Our goal is to show that creative coding is a rewarding way of learning mathematics, with a creative approach.Proyecto, desarrollo y valoración en la UPC de un caso de feedforwarding en campus virtual
http://hdl.handle.net/2117/85557
Proyecto, desarrollo y valoración en la UPC de un caso de feedforwarding en campus virtual
Fabregat Fillet, Jaume; Pelayo Melero, Ignacio Manuel; Valero Baya, Jordi; Ornat Longarón, Cèsar; Achaerandio Puente, María Isabel; Pineda Soler, Eloi; Buenestado Caballero, Pablo
Docentes de UPC, UB, UAB, UIB, UOC y URV investigamos sobre una evaluación formativa "feedforwarding", que realimente de inmediato, que no se limite al "correcto-incorrecto", que guíe más que resuelva, que sea suficientemente individualizada, que motive reflexión - acción y que genere un trabajo sostenible para alumnos y profesores.
La aplicación en la UPC ha recaído sobre "Matemáticas" del primer cuatrimestre en la Escuela Superior de Agricultura de Barcelona. Se ha diseñado una experiencia transferible a más asignaturas, que usa apoyos de NTIC y que permite analizar eventuales logros resultantes de su despliegue. Para fomentar el aprendizaje se han administrado cuestionarios sobre la disciplina, con y sin realimentación. Los estudiantes han considerado primero un cuestionario con realimentación reiterada hasta que responden bien todas las preguntas y, posteriormente, han afrontado un cuestionario similar sin realimentación.
Se ha actuado sobre unos doscientos estudiantes, con cinco cuestionarios dobles generados con WIRIS (correspondientes a los cinco temas de la asignatura), empleando la versión Moodle 2.6.2. Se ha estudiado la contribución al rendimiento académico y la satisfacción de los agentes, constatándose aumento de dedicación a la materia, mejoras (no duraderas) en el aprendizaje y valoración positiva del paso dado.
Tue, 12 Apr 2016 11:42:44 GMThttp://hdl.handle.net/2117/855572016-04-12T11:42:44ZFabregat Fillet, JaumePelayo Melero, Ignacio ManuelValero Baya, JordiOrnat Longarón, CèsarAchaerandio Puente, María IsabelPineda Soler, EloiBuenestado Caballero, PabloDocentes de UPC, UB, UAB, UIB, UOC y URV investigamos sobre una evaluación formativa "feedforwarding", que realimente de inmediato, que no se limite al "correcto-incorrecto", que guíe más que resuelva, que sea suficientemente individualizada, que motive reflexión - acción y que genere un trabajo sostenible para alumnos y profesores.
La aplicación en la UPC ha recaído sobre "Matemáticas" del primer cuatrimestre en la Escuela Superior de Agricultura de Barcelona. Se ha diseñado una experiencia transferible a más asignaturas, que usa apoyos de NTIC y que permite analizar eventuales logros resultantes de su despliegue. Para fomentar el aprendizaje se han administrado cuestionarios sobre la disciplina, con y sin realimentación. Los estudiantes han considerado primero un cuestionario con realimentación reiterada hasta que responden bien todas las preguntas y, posteriormente, han afrontado un cuestionario similar sin realimentación.
Se ha actuado sobre unos doscientos estudiantes, con cinco cuestionarios dobles generados con WIRIS (correspondientes a los cinco temas de la asignatura), empleando la versión Moodle 2.6.2. Se ha estudiado la contribución al rendimiento académico y la satisfacción de los agentes, constatándose aumento de dedicación a la materia, mejoras (no duraderas) en el aprendizaje y valoración positiva del paso dado.On middle cube graphs
http://hdl.handle.net/2117/85344
On middle cube graphs
Dalfó Simó, Cristina; Fiol Mora, Miquel Àngel; Mitjana Riera, Margarida
We study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors).
Thu, 07 Apr 2016 10:46:49 GMThttp://hdl.handle.net/2117/853442016-04-07T10:46:49ZDalfó Simó, CristinaFiol Mora, Miquel ÀngelMitjana Riera, MargaridaWe study a family of graphs related to the $n$-cube. The middle cube graph of parameter k is the subgraph of $Q_{2k-1}$ induced by the set of vertices whose binary representation has either $k-1$ or $k$ number of ones. The middle cube graphs can be obtained from the well-known odd graphs by doubling their vertex set. Here we study some of the properties of the middle cube graphs in the light of the theory of distance-regular graphs. In particular, we completely determine their spectra (eigenvalues and their multiplicities, and associated eigenvectors).The diameter of cyclic Kautz digraphs
http://hdl.handle.net/2117/85343
The diameter of cyclic Kautz digraphs
Böhmová, Katerina; Dalfó Simó, Cristina; Huemer, Clemens
A prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and degree there is no other digraph with a smaller diameter. This new family is called modified cyclic digraphs MCK(d,l) and it is derived from the Kautz digraphs K(d,l). It is well-known that the Kautz digraphs K(d,l) have the smallest diameter among all digraphs with their number of vertices and degree. Here we define the cyclic Kautz digraphs CK(d,l), whose vertices are labeled by all possible sequences a1…al of length l , such that each character ai is chosen from an alphabet containing d+1 distinct symbols, where the consecutive characters in the sequence are different (as in Kautz digraphs), and now also requiring that a1¿al. The cyclic Kautz digraphs CK(d,l) have arcs between vertices a1a2…al and a2…alal+1, with a1¿al, a2¿al+1, and ai¿ai+1 for i=1,…,l-1. The cyclic Kautz digraphs CK(d,l) are subdigraphs of the Kautz digraphs K(d,l). We give the main parameters of CK(d,l) (number of vertices, number of arcs, and diameter). Moreover, we construct the modified cyclic Kautz digraphs MCK(d,l) to obtain the same diameter as in the Kautz digraphs, and we show that MCK(d,l) are d -out-regular. Finally, we compute the number of vertices of the iterated line digraphs of CK(d,l).
Thu, 07 Apr 2016 10:39:47 GMThttp://hdl.handle.net/2117/853432016-04-07T10:39:47ZBöhmová, KaterinaDalfó Simó, CristinaHuemer, ClemensA prominent problem in Graph Theory is to find extremal graphs or digraphs with restrictions in their diameter, degree and number of vertices. Here we obtain a new family of digraphs with minimal diameter, that is, given the number of vertices and degree there is no other digraph with a smaller diameter. This new family is called modified cyclic digraphs MCK(d,l) and it is derived from the Kautz digraphs K(d,l). It is well-known that the Kautz digraphs K(d,l) have the smallest diameter among all digraphs with their number of vertices and degree. Here we define the cyclic Kautz digraphs CK(d,l), whose vertices are labeled by all possible sequences a1…al of length l , such that each character ai is chosen from an alphabet containing d+1 distinct symbols, where the consecutive characters in the sequence are different (as in Kautz digraphs), and now also requiring that a1¿al. The cyclic Kautz digraphs CK(d,l) have arcs between vertices a1a2…al and a2…alal+1, with a1¿al, a2¿al+1, and ai¿ai+1 for i=1,…,l-1. The cyclic Kautz digraphs CK(d,l) are subdigraphs of the Kautz digraphs K(d,l). We give the main parameters of CK(d,l) (number of vertices, number of arcs, and diameter). Moreover, we construct the modified cyclic Kautz digraphs MCK(d,l) to obtain the same diameter as in the Kautz digraphs, and we show that MCK(d,l) are d -out-regular. Finally, we compute the number of vertices of the iterated line digraphs of CK(d,l).