The (a,b,s,t)-diameter of graphs: a particular case of conditional diameter

The conditional diameter of a connected graph $\Gamma=(V,E)$ is defined as follows: given a property ${\cal P}$ of a pair $(\Gamma_1, \Gamma_2)$ of subgraphs of $\Gamma$, the so-called \emph{conditional diameter} or ${\cal P}$-{\em diameter} measures the maximum distance among subgraphs satisfying ${\cal P}$. That is, $$D_{{\cal P}}(\Gamma):=\max_{\Gamma_1, \Gamma_2\subset \Gamma} \{\partial(\Gamma_1, \Gamma_2): \Gamma_1, \Gamma_2 \quad {\rm satisfy }\quad {\cal P}\}.$$ In this paper we consider the conditional diameter in which ${\cal P}$ requires that $\delta(u)\ge \alpha$ for all $u\in V(\Gamma_1)$, $\delta(v)\ge \beta$ for all $v\in V(\Gamma_2)$, $| V(\Gamma_1)| \ge s$ and $| V(\Gamma_2)| \ge t$ for some integers $1\le s,t\le |V|$ and $\delta \le \alpha, \beta \le \Delta$, where $\delta(x)$ denotes the degree of a vertex $x$ of $\Gamma$, $\delta$ denotes the minimum degree and $\Delta$ the maximum degree of $\Gamma$. The conditional diameter obtained is called $(\alpha ,\beta, s,t)$-\emph{diameter}. We obtain upper bounds on the $(\alpha ,\beta, s,t)$-diameter by using the $k$-alternating polynomials on the mesh of eigenvalues of an associated weighted graph. The method provides also bounds for other parameters such as vertex separators

Locating-dominating sets and identifying codes in graphs of girth at least 5

Locating-dominating sets and identifying codes are two closely related notions in the area of separating systems. Roughly speaking, they consist in a dominating set of a graph such that every vertex is uniquely identified by its neighbourhood within the dominating set. In this paper, we study the size of a smallest locating-dominating set or identifying code for graphs of girth at least 5 and of given minimum degree. We use the technique of vertex-disjoint paths to provide upper bounds on the minimum size of such sets, and construct graphs who come close to meet these bounds.Comment: 20 pages, 9 figure

La feria de la astronomía

La Feria de Astronomía es una experiencia desarrollada como actividad de un Taller de Astronomía que impartí en el IES Viera y Clavijo de La Laguna, Tenerife. Esta asignatura tiene un marcado carácter pluridisciplinar pues se “abastece” de interesantes parcelas: las matemáticas, la física, la mitología, etc. Observar el cielo, orientarse, conocer y localizar las constelaciones, saber del Sol y de la Luna, estudiar las cosmologías, etc. son conocimientos que atraen y “enganchan”. Con la ayuda de la Feria, se pudieron compartir con el resto de los estudiantes del centro. Los distintos kioscos y el acompañamiento durante el recorrido fueron atendidos por el alumnado del Taller que consiguió el objetivo propuesto según se desprendió de las encuestas pasadas a los asistentes. En este artículo se explica el proceso que, obviamente, puede ser trasladado a cualquier sitio

A formulation of a (q+1,8)-cage

Let $q\ge 2$ be a prime power. In this note we present a formulation for obtaining the known $(q+1,8)$-cages which has allowed us to construct small $(k,g)$--graphs for $k=q-1, q$ and $g=7,8$. Furthermore, we also obtain smaller $(q,8)$-graphs for even prime power $q$.Comment: 14 pages, 2 figure

Attitudes of residents towards tourism. The case of Benalmadena, Spain

Tourism is consumed in the place of production causing a series of impacts. These effects caused by tourism can be perceived positively or negatively by residents. The objective of this study is to analyze the attitude of the residents from the impacts of tourism in the town of Benalmádena, Spanish town that is located within the Costa del Sol. We used a quantitative methodology and we have carried out an extensive survey of 770 residents. Information has been collected through questionnaires and there have been exploratory and ANOVA analysis. The results are: the economic benefits are the most important elements sought and valued by the local population. However, they also recognize the negative effects of this dimension, in the same way as with the socio-cultural and environmental impacts.This study is to analyze the attitude of the residents from the impacts of tourism in the town of Benalmádena, Spanish. This is a mature destination framed in a pattern of sun and beach in 2012 has a total of 10,885 hotel places. Benalmádena tourism has a significant oscillation throughout the year, peaking in the months of July to September and the minimum between December and February.Universidad de Málaga. Campus de Excelencia Internacional Andalucía Tech

Martin Gardner, inspirador de la Expo 2000

La matemática recreativa estará siempre en deuda con Martin Gardner porque a él se debe, en gran parte, la difusión de muchos juegos y otros entretenimientos que, en casi todos los casos habían sido inventados por otros. Pero no solo los difundió sino que profundizó en ellos y amplió sus posibilidades hasta límites insospechados. Muchas de esas aportaciones, pasaron del papel a materiales manipulables para formar parte de la exposición itinerante Expo 2000