Almost Self-Centered Median And Chordal Graphs

Almost self-centered graphs were recently introduced as the graphs with exactly two non-central vertices. In this paper we characterize almost selfcentered graphs among median graphs and among chordal graphs. In the first case P4 and the graphs obtained from hypercubes by attaching to them a single leaf are the only such graphs. Among chordal graph the variety of almost self-centered graph is much richer, despite the fact that their diameter is at most 3. We also discuss almost self-centered graphs among partial cubes and among k-chordal graphs, classes of graphs that generalize median and chordal graphs, respectively. Characterizations of almost self-centered graphs among these two classes seem elusive

The median function on graphs with bounded profiles

The median of a profile = (u1, . . . , uk ) of vertices of a graph G is the set of vertices x that minimize the sum of distances from x to the vertices of . It is shown that for profiles with diameter the median set can be computed within an isometric subgraph of G that contains a vertex x of and the r -ball around x, where r > 2 − 1 − 2 /| |. The median index of a graph and r -joins of graphs are introduced and it is shown that r -joins preserve the property of having a large median index. Consensus strategies are also briefly discussed on a graph with bounded profiles.

Median computation in graphs using consensus strategies

Following the Majority Strategy in graphs, other consensus strategies, namely Plurality Strategy, Hill Climbing and Steepest Ascent Hill Climbing strategies on graphs are discussed as methods for the computation of median sets of pro¯les. A review of algorithms for median computation on median graphs is discussed and their time complexities are compared. Implementation of the consensus strategies on median computation in arbitrary graphs is discussed

Equal opportunity networks, distance-balanced graphs, and Wiener game

Given a graph G and a set X ⊆ V(G), the relative Wiener index of X in G is defined as WX (G) = {u,v}∈X 2  dG(u, v) . The graphs G (of even order) in which for every partition V(G) = V1 +V2 of the vertex set V(G) such that |V1| = |V2| we haveWV1 (G) = WV2 (G) are called equal opportunity graphs. In this note we prove that a graph G of even order is an equal opportunity graph if and only if it is a distance-balanced graph. The latter graphs are known by several characteristic properties, for instance, they are precisely the graphs G in which all vertices u ∈ V(G) have the same total distance DG(u) = v∈V(G) dG(u, v). Some related problems are posed along the way, and the so-called Wiener game is introduced.

Fair Sets of Some Classes of Graphs

Given a non empty set S of vertices of a graph, the partiality of a vertex with respect to S is the di erence between maximum and minimum of the distances of the vertex to the vertices of S. The vertices with minimum partiality constitute the fair center of the set. Any vertex set which is the fair center of some set of vertices is called a fair set. In this paper we prove that the induced subgraph of any fair set is connected in the case of trees and characterise block graphs as the class of chordal graphs for which the induced subgraph of all fair sets are connected. The fair sets of Kn, Km;n, Kn e, wheel graphs, odd cycles and symmetric even graphs are identi ed. The fair sets of the Cartesian product graphs are also discussed

Consensus strategies for signed profiles on graphs

The median problem is a classical problem in Location Theory: one searches for a location that minimizes the average distance to the sites of the clients. This is for desired facilities as a distribution center for a set of warehouses. More recently, for obnoxious facilities, the antimedian was studied. Here one maximizes the average distance to the clients. In this paper the mixed case is studied. Clients are represented by a profile, which is a sequence of vertices with repetitions allowed. In a signed profile each element is provided with a sign from f+; g. Thus one can take into account whether the client prefers the facility (with a + sign) or rejects it (with a sign). The graphs for which all median sets, or all antimedian sets, are connected are characterized. Various consensus strategies for signed profiles are studied, amongst which Majority, Plurality and Scarcity. Hypercubes are the only graphs on which Majority produces the median set for all signed profiles. Finally, the antimedian sets are found by the Scarcity Strategy on e.g. Hamming graphs, Johnson graphs and halfcubes

Median graphs, the remoteness function, periphery transversals, and geodetic number two

A periphery transversal of a median graph G is introduced as a set of vertices that meets all the peripheral subgraphs of G. Using this concept, median graphs with geodetic number 2 are characterized in two ways. They are precisely the median graphs that contain a periphery transversal of order 2 as well as the median graphs for which there exists a profile such that the remoteness function is constant on G. Moreover, an algorithm is presented that decides in O(mlog n) time whether a given graph G with n vertices and m edges is a median graph with geodetic number 2. Several additional structural properties of the remoteness function on hypercubes and median graphs are obtained and some problems listed

Conceptual structures represented by conceptual graphs and formal concept analysis

Conceptual Graphs and Formal Concept Analysis have in common basic concerns: the focus on conceptual structures, the use of diagrams for supporting communication, the orientation by Peirce's Pragmatism, and the aim of representing and processing knowledge. These concerns open rich possibilities of interplay and integration. We discuss the philosophical foundations of both disciplines, and analyze their specific qualities. Based on this analysis, we discuss some possible approaches of interplay and integration.

Meshing highly regular structures: The case of super carbon nanotubes of arbitrary order

Mesh generation is an important step inmany numerical methods.We present the “HierarchicalGraphMeshing” (HGM)method as a novel approach to mesh generation, based on algebraic graph theory.The HGM method can be used to systematically construct configurations exhibiting multiple hierarchies and complex symmetry characteristics. The hierarchical description of structures provided by the HGM method can be exploited to increase the efficiency of multiscale and multigrid methods. In this paper, the HGMmethod is employed for the systematic construction of super carbon nanotubes of arbitrary order, which present a pertinent example of structurally and geometrically complex, yet highly regular, structures. The HGMalgorithm is computationally efficient and exhibits good scaling characteristics. In particular, it scales linearly for super carbon nanotube structures and is working much faster than geometry-based methods employing neighborhood search algorithms. Its modular character makes it conducive to automatization. For the generation of a mesh, the information about the geometry of the structure in a given configuration is added in a way that relates geometric symmetries to structural symmetries. The intrinsically hierarchic description of the resulting mesh greatly reduces the effort of determining mesh hierarchies for multigrid and multiscale applications and helps to exploit symmetry-related methods in the mechanical analysis of complex structures.

Importancia y necesidad de regular las intervenciones educativas de la policía local en materia de tráfico.

Resumen tomado de la publicación

CIP-OSN; Networks as Graphs

Curriculum Innovation Programme - Online Social Networks (UOSM2012) - Networks as Graphs

Gauss y el polígono regular de 17 lados.

Se recoge uno de los concepto más destacados de Carl Friedrich Gauss como es el polígono regular de 17 lados. Se estudian los diferentes pasos que llevan a la construcción de este polígono con los diferentes cálculos aritméticos.

Les estrategies d'interacció del professor amb l'alumne sord a l'aula regular. Criteris per a la seva utilització. 'Las estrategias de interacción del profesor con el alumno sordo en el aula regular. Criterios para su utilización'.

Conocer la realidad comunicativa que se produce en el aula regular entre profesor y alumno sordo; identificar los patrones que gobiernan los diferentes estilos comunicativos del profesor y sus efectos sobre el habala del alumno; y, plantear una propuesta del modelo para el análisis y la optimización del estilo comunicativo del profesor en el aula integradora.. Primera fase: 20 profesores y 20 alumnos (16-18 años) de 20 aulas de escuelas de integración. Segunda fase: 6 profesors y 6 alumnos (3 grupo control, 3 grupo experimental) de diversos cursos de EGB, de 6 aulas de escuelas de integración. Elabora un marco teórico, expone los conceptos fundamentales de la integración del alumno sordo en nuestro pais, describe de forma global las particularidades comunicativas que suelen caracterizar a los sujetos con pérdidas auditivas, revisa las aportaciones teóricas, expone las investigaciones llevadas a cabo con anterioridad. El trabajo de investigación se divide en 2 fases: en la primera obtiene un perfil que muestra los principales parámetros de la interacción entre el profesor y el alumno sordo en el aula de integración, en la segunda fase aplica el programa de ciclo de aprendizaje al grupo experimental para modificar los parámetros observados en la anterior fase y observa las diferencias encontradas con respecto al grupo control. . Entrevistas. Cuestionario. Transcripción. Cámara de video. Prueba de la historia empleada por Rams-Pott. Cuaderno de registro. . Porcentajes. Análisis descriptivo. Análisis comparativo. Distribución de frecuencias. Sistema de codificación Clan. . Existe una relación entre las estrategias de trabajo utilizadas por el profesor con el alumno sordo y la actitud ideológica del profesor hacia la integración. El comportamiento docente observado en realción a las situaciones de reparación didáctica está vinculado a la experiencia del docente con el alumno. Ante errores de ejecución o producción las estrategias más empleadas son de tipo restrictivo y ante errores de comprensión las estrategias son más expansivas. Cualitativamente mejora el perfil interactivo de los profesores y alumnos del grupo experimental. . Es necesario poner en marcha nuevas investigaciones que respondan a las siguientes preguntas: +Cuáles son los mecanismos de adaptación del alumno a los diversos patrones interactivos mostrados por el profesor?, +Cómo influye el modelo comunicativo del profesor en el intercambio entre los compañeros oyentes y el propio sordo?.

Equivalencia entre cualquier polígono regular o irregular y un triángulo equilátero.

Resumen basado en el de la publicación

Una revisión al diseño curricular nacional de educación básica regular del Perú en el nivel secundario y de Área de Matemáticas.

Resumen basado en el de la publicación. Resumen en inglés