The resolving number of a graph

We study a graph parameter related to resolving sets and metric dimension, namely the resolving number, introduced by Chartrand, Poisson and Zhang. First, we establish an important difference between the two parameters: while computing the metric dimension of an arbitrary graph is known to be NP-hard, we show that the resolving number can be computed in polynomial time. We then relate the resolving number to classical graph parameters: diameter, girth, clique number, order and maximum degree. With these relations in hand, we characterize the graphs with resolving number 3 extending other studies that provide characterizations for smaller resolving number.Comment: 13 pages, 3 figure

Resolving sets for breaking symmetries of graphs

This paper deals with the maximum value of the difference between the determining number and the metric dimension of a graph as a function of its order. Our technique requires to use locating-dominating sets, and perform an independent study on other functions related to these sets. Thus, we obtain lower and upper bounds on all these functions by means of very diverse tools. Among them are some adequate constructions of graphs, a variant of a classical result in graph domination and a polynomial time algorithm that produces both distinguishing sets and determining sets. Further, we consider specific families of graphs where the restrictions of these functions can be computed. To this end, we utilize two well-known objects in graph theory: $k$-dominating sets and matchings.Comment: 24 pages, 12 figure

Introducció: El debat entre W.K. Clifford i William James

Introducció al debat entre Cliiford i James i a la traducció dels seus articles "L'ètica de la creença" i "La voluntat de creure"

Graph theory with an introduction to algebraic graph theory

Firstly, we shall start with an introduction to the main topics in Graph Theory with special emphasis in connectivity, colorability and planarity. The, we shall continue with the firsts concepts in Algebraic Graph Theory. Algebraic Graph Theory uses algebraic techniques to study properties of graphs. We shall see several examples of those techniques, covering, for instance the fundamental group of a graph, several polynomials associated to graphs, and the spectra of a graph. seeing how those algebraic tools provide information about the properties of the graph.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Annihilacionismo y la erradicación de todo pecado

El annihilacionismo afirma que la muerte terrenal va seguida de un juicio divino tras el cual los pecadores son condenados a una segunda (e irrevocable) muerte, mientras que aquellos que han vivido su vida terrena de acuerdo con los preceptos de Dios son bendecidos con una existencia eterna en el cielo. El objetivo de este ensayo es mostrar que, contrariamente a lo que los defensores del annihilacionismo argumentan, la tesis que la victoria de Dios sobre el mal requiere de la completa erradicación de todo pecado no es suficiente, por sí sola, para justificar la doctrina annihilacionista.Annihilationism claims that earthly death is followed by a divine judgment after which the wicked are condemned to a second (and irrevocable) death, while those who have lived their earthly life according to God's commands are blessed with a heavenly eternal existence. The aim of this essay is to show that, contrary to what defenders of annihilationism argue, the claim that God's victory over evil requires the complete eradication of all sin does not suffice alone to justify annihilationism.peerReviewe

Vibrational assignments of two polymorphic forms of metaxolone by using DFT calculations and the SQM methodology

A theoretical study has been performed on the musclerelaxant 5-[(3, 5-dimethylphenoxy)methyl]-1,3-oxazolidin-2-one, of generic name metaxolone (MTX), by using the hybridB3LYP/6-31G calculations in the gas phase and theexperimental available infrared and Raman spectra in thesolid phase. Three C1, C2 and C3 isomers were found in thepotential energy surface (PES) but only two of them, C1 andC2 correspond to those experimentally reported polymorphicforms A and B, respectively. The absence of C3 isomer couldbe easily explained by the quite high values in the dihedralC5-C7-O2-C9 and O1-C5-C7-O2 angles different from thoseexperimental structures reported for the two polymorphicforms A and B of MTX. On the other hand, the higher bondorders values together with the high topological propertiesobserved for the oxazolidinone ring of C1 could possiblysupport their existence despite this isomer has highest energythan C2 and C3. The natural bond orbital (NBO) analysesreveal the high stabilities of C1 and C2 while the atoms inmolecules(AIM) study suggests that the ringdimethylphenoxy-methyl practically do not have influence onthe properties of MTX. The frontier orbitals show that theisomers of MTX have reactivities and electrophilicity indexessimilar to antiviral thymidine while their nucleophilicityindexes present values closer to antimicrobial thione. Inaddition, the complete vibrational assignments of those twostable isomers were performed by using the experimentalavailable FT-IR and FT-Raman spectra, their normal internalcoordinates,the scaled quantum mechanical force field(SQMFF) methodology and the Molvib program.Theharmonic force fields for the two isomers and theircorresponding force constants were also reported. The forceconstants values are in agreement with values reported in theliterature for species with similar groups.Fil: Iramain, Maximiliano Alberto. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química Inorgánica; ArgentinaFil: Márquez, María J.. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química Inorgánica; ArgentinaFil: Ledesma, Ana Estela. Universidad Nacional de Santiago del Estero. Facultad de Cs.exactas y Tecnologías. Departamento de Física y Química; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; ArgentinaFil: Brandan, Silvia Antonia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Tucumán. Facultad de Bioquímica, Química y Farmacia. Instituto de Química Inorgánica; Argentin

“DISTANCIA DE LA PIEL AL ESPACIO PERIDURAL SEGÚN EL INDICE DE MASA CORPORAL EN EL PACIENTE PROGRAMADO PARA CIRUGIA ELECTIVA EN CENTRO MEDICO ISSEMYM ECATEPEC EN EL PERIODO DE MAYO DEL 2012 A SEPTIEMBRE DEL 2012”

La Anestesia Neuroaxial es una técnica ampliamente utilizada, debido a las numerosas ventajas que esta ofrece. El Bloqueo Peridural o Epidural también conocido, presenta diversas aplicaciones: para anestesia quirúrgica, analgesia postoperatoria y para manejo de dolor crónico casos donde la anestesia general balanceada se encuentra contraindicada

An aperiodic tiles machine

The results we introduce in this work lead to get an algorithm which produces aperiodic sets of tiles using Voronoi diagrams. This algorithm runs in optimal worst-case time O(nlogn). Since a wide range of new examples can be obtained, it could shed some new light on non-periodic tilings. These examples are locally isomorphic and exhibit the 5-fold symmetry which appears in Penrose tilings and quasicrystals. Moreover, we outline a similar construction using Delaunay triangulations and propose some related open problems