Repositório Comunidade: Informática e Matemática
http://hdl.handle.net/10198/193
Informática e Matemática2015-07-01T01:59:11ZThe construction of the poset of regular execeptional graphs using equitable partitions
http://hdl.handle.net/10198/10902
Título: The construction of the poset of regular execeptional graphs using equitable partitions
Autor: Barbedo, Inês; Cardoso, Domingos M.; Rama, Paula
Resumo: An exceptional graph is a connected graph with least eigenvalue greater than or equal to -2 which is not a generalized line graph.
It is shown that the set of regular exceptional graphs is partitioned in three layers. A (k,t)-regular set is a subset of the vertices of a graph, inducing a k-regular subgraph such that every vertex not in the subset has t neighbors in it. A new recursive construction of regular exceptional graphs is proposed, where each regular exceptional graph of the first and the second layer is constructed by a (0,2)-regular set extension.
In this talk we present an algorithm based on this recursive construction and show that this technique induces a partial order relation on the set of regular exceptional graphs. The process of extending a graph is reduced to the construction of the incidence matrix of a combinatorial 1-design, considering several rules to prevent the production of isomorphic graphs, and we show that each regular exceptional graph has an equitable partition which, by this construction technique, is extended with a new element, the set of the additional vertices. The recursive construction is generalized to the construction of arbitrary families of regular graphs, by extending a regular graph G with another regular graph H such that V(H) is a (k,t)-regular set of the regular graph produced. This technique is used to construct the exceptional regular graphs of the third layer.
The Hasse diagrams of the posets of the three layers are presented.2013-01-01T00:00:00ZThe poset structure of the regular exceptional graphs
http://hdl.handle.net/10198/10889
Título: The poset structure of the regular exceptional graphs
Autor: Barbedo, Inês; Cardoso, Domingos M.; Rama, Paula
Resumo: An exceptional graph is a connected graph with least eigenvalue greater than or equal to -2 which is not a generalized line graph. It is shown that the set of regular exceptional graphs is partitioned in three layers.
A (k,t)-regular set is a subset of the vertices of a graph, inducing a k-regular subgraph such that every vertex not in the
subset has t neighbors in it. A new recursive construction of regular exceptional graphs is proposed, where each
exceptional regular graph is constructed by a (0,2)-regular set extension. These extensions induce a partial order on the set on the exceptional
graphs in each layer. Based on this construction, an algorithm to produce the regular exceptional graphs of the first and second layer is introduced and
the corresponding poset is presented, using its Hasse diagram. The process of extending a graph is reduced to the construction of the incidence matrix of a combinatorial 1-design, considering several rules to prevent the production of isomorphic graphs.
A generalization of this recursive procedure to the construction of families of regular graphs, where each regular graph is obtained by a (k,t)-regular extension defined by a k-regular graph H such that V(H) is a (k,t)-regular set of the extended
regular graph, is introduced. Finally, some results on the multiplicity of the eigenvalue k-t are presented.2013-01-01T00:00:00ZAn approach about health games to social network environment
http://hdl.handle.net/10198/10782
Título: An approach about health games to social network environment
Autor: Pinho, Anabela; Paredes, Hugo; Zagalo, Nelson
Resumo: The need for contact, sharing and socializing is
part of human nature, so that the community's role is vital to
the survival of the species. With the development of
Information and Communication Technologies and their
influence on society and everyday life, led the search for new
ways to build relationships and create communities among
people, creating virtual communities; turn social networks
emerge as new forms of association that respond to more
complex understanding of human interaction in a way that
the wider community; these to promote your main goal,
more integrated into the games as a tool of socialization. The
impact of current games at various levels, as the social and
economic development, and its applicability in various fields,
it becomes important to analyze the contribution of the
community. It is intended in this article, a description of the
factors that motivate this research to a later stage to develop
the proposed objectives: to analyze the new social reality and
develop a model that allows adapting the health games to
social games in order to foster the creation / sustainability of
communities based on social networks, aiming to raise
awareness of health issues, increasing knowledge and
sharing of experiences of members of communities.2011-01-01T00:00:00ZIn search of a poset structure to the regular exceptional graphs
http://hdl.handle.net/10198/10677
Título: In search of a poset structure to the regular exceptional graphs
Autor: Barbedo, Inês; Cardoso, Domingos M.; Rama, Paula
Resumo: A (k,t)-regular set is a subset of the vertices of a graph, inducing a k -regular subgraph such that every vertex not in the subset has t neighbors in it.
An exceptional graph is a connected graph with least eigenvalue greater than or equal to -2 which is not a generalized line graph, and it is shown that the set of regular exceptional graphs is partitioned in three layers. The idea of a recursive construction of regular exceptional graphs is proposed in [1]. With a new technique we prove that all regular exceptional graphs from the 1st and 2nd layer could be produced by this technique.
The new recursive technique is based on the construction of families of regular graphs, where each regular graph is obtained by a (k,t)-extension defined by a k- regular graph H such that V(H) is a (k,t)-regular set of the extended regular graph. The process of extending a graph is reduced to the construction of the incidence matrix of a combinatorial 1-design, and these extensions induce a partial order.
Considering several rules to reduce the production of isomorphic graphs, each exceptional regular graph is constructed by a (0,2)-extension. Based on this construction, an algorithm to produce the regular exceptional graphs of the 1st and 2nd layer is introduced and the corresponding poset is presented, using its Hasse diagram.2013-01-01T00:00:00Z