Repositório Colecção:
http://hdl.handle.net/10198/3282
2015-04-25T08:57:23ZThe 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.2013-01-01T00:00:00ZA ubiquidade e a contextualização no acesso à informação e serviços turísticos
http://hdl.handle.net/10198/8505
Título: A ubiquidade e a contextualização no acesso à informação e serviços turísticos
Autor: Cunha, Carlos R.; Carvalho, Aida; Santos, Arlindo
Resumo: Com a distinção da região do Alto Douro Vinhateiro a Património da Humanidade, na categoria de Paisagem Cultural, em dezembro de 2001, a região teve eco internacional,
alcançando nova visibilidade. A natureza pristina convida o visitante a conhecer todo este património, transformando-o num recurso turístico que necessita de ser explicado e/ou interpretado (a história, as tradições, os artefactos, a arte, entre outros) de forma célere assente no pressuposto da ubiquidade de acesso à informação.2013-01-01T00:00:00Z