On global location-domination in graphs

A dominating set $S$ of a graph $G$ is called locating-dominating, LD-set for short, if every vertex $v$ not in $S$ is uniquely determined by the set of neighbors of $v$ belonging to $S$. Locating-dominating sets of minimum cardinality are called $LD$-codes and the cardinality of an LD-code is the location-domination number $\lambda(G)$. An LD-set $S$ of a graph $G$ is global if it is an LD-set of both $G$ and its complement $\overline{G}$. The global location-domination number $\lambda_g(G)$ is the minimum cardinality of a global LD-set of $G$. In this work, we give some relations between locating-dominating sets and the location-domination number in a graph and its complement.Comment: 15 pages: 2 tables; 8 figures; 20 reference

Escoles i programes acadèmics a la Barcelona del segle XV. L'escola de mestre Ramon Llull i l'ensenyament de disciplines gramaticals i d'arts

During the XV century continued in Barcelona the union of education professionals to the formation of societys for private schools administration, different from the public ones (the cathedral and de city of Barcelona ones) and reading and writing education (primary education) and grammar and arts (trivium and quadrivium, secundary education). The academic programme of these schools and textbooks used were set up and regulated on these agreements or society contracts. On a documentary appendix are published 15 documents about the school called Escola de Mestre Ramon Llull and the academic programmes used in these schools