PUERTAS , María Luz

This paper initiates a study on the problem of computing the difference between the metric dimension and the determining number of graphs. We provide new proofs and results on the determining number of trees and Cartesian products of graphs, and establish some lower bounds on the difference between the two parameters.

MATHEMATICS TEACHING RESEARCH JOURNAL 186 SUMMER 2022 Vol 14 no 2 This content is covered by a Creative Commons license, Attribution-NonCommercial-ShareAlike 4.0 International (CC BY-NC-SA 4.0). This license allows re-users to distribute, remix, adapt, and build upon the material in any medium or format for noncommercial purposes only, and only...

This work is devoted to exploring proof abilities in Graph Theory of undergraduate students of the Degree in Computer Engineering and Technology of the University of Seville. To do this, we have designed a questionnaire consisting of five open-ended items that serve as instrument to collect data concerning their proof skills when dealing with...

En este trabajo exploramos las habilidades de reconocimiento en teoría de grafos que poseen estudiantes universitarios del grado en Ingeniería Informática-Tecnologías Informáticas de la Universidad de Sevilla. Para ello, diseñamos un cuestionario que empleamos como instrumento de recogida de datos, los cuales son posteriormente analizados...

The need to develop consistent theoretical frameworks for the teaching and learning of discrete mathematics, specifically of graph theory, has attracted the attention of the researchers in mathematics education. Responding to this demand, the scope of the Van Hiele model has been extended to the field of graphs through a proposal of four levels...

This work provides a characterization of the learning of graph theory through the lens of the van Hiele model. For this purpose, we perform a theoretical analysis structured through the processes of reasoning that students activate when solving graph theory problems: recognition, use and formulation of definitions, classification, and proof. We...

We study the problem of augmenting the locus N of a plane Euclidean network N by inserting iteratively a finite set of segments, called shortcut set, while reducing the diameter of the locus of the resulting network. We first characterize the existence of shortcut sets, and compute shortcut sets in polynomial time providing an upper bound on...

We study the problem of augmenting the locus N of a plane Euclidean network N by in- serting iteratively a finite set of segments, called shortcut set , while reducing the diameterof the locus of the resulting network. There are two main differences with the classicalaugmentation problems: the endpoints of the segments are allowed to be...