Minimal strong digraphs

We introduce adequate concepts of expansion of a digraph to obtain a sequential construction of minimal strong digraphs. We obtain a characterization of the class of minimal strong digraphs whose expansion preserves the property of minimality. We prove that every minimal strong digraph of order nmayor que=2 is the expansion of a minimal strong digraph of order n-1 and we give sequentially generative procedures for the constructive characterization of the classes of minimal strong digraphs. Finally we describe algorithms to compute unlabeled minimal strong digraphs and their isospectral classes.

Design and implementation of a mathematical videogame

This paper presents videogames as a very useful tool in high studies with respect to mathematical matters. It describes the implementation of a videogame developed by its authors which makes it possible for students to reinforce mathematical concepts in a motivating environment. With this work we intend to contribute to the process of engaging a bigger number of university teaching professionals and researchers in the use of serious games and the study of their theoretical frameworks, design, development and application of scientific education. With this idea the authors of the present paper have created and developed the videogame “The Math Castle” which consists in a series of tests through which various aspects of Mathematics are dealt with, especially in the areas of Discrete Mathematics, which due to its nature can be particularly well adapted to this kind of activity, Analysis or Geometry. In this paper there lies a complete description of the game developed and the results obtained with it.