Closed models, strongly connected components and Euler graphs

In this paper, we continue our study of closed models defined in categories of graphs. We construct a closed model defined in the cat-egory of directed graphs which characterizes the strongly connected components. This last notion has many applications, and it plays an important role in the web sear...

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Autor principal: Aristide,Tsemo
Lenguaje:English
Publicado: Universidad Católica del Norte, Departamento de Matemáticas 2016
Acceso en línea:http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000200001
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spelling oai:scielo:S0716-091720160002000012016-05-30Closed models, strongly connected components and Euler graphsAristide,TsemoIn this paper, we continue our study of closed models defined in categories of graphs. We construct a closed model defined in the cat-egory of directed graphs which characterizes the strongly connected components. This last notion has many applications, and it plays an important role in the web search algorithm of Brin and Page, the foun-dation of the search engine Google. We also show that for this closed model, Euler graphs are particular examples of cofibrant objects. This enables us to interpret in this setting the classical result of Euler which states that a directed graph is Euleurian if and only if the in degree and the out degree of every of its nodes are equal. We also provide a cohomological proof of this last result.info:eu-repo/semantics/openAccessUniversidad Católica del Norte, Departamento de MatemáticasProyecciones (Antofagasta) v.35 n.2 20162016-06-01text/htmlhttp://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000200001en10.4067/S0716-09172016000200001
institution Scielo Chile
collection Scielo Chile
language English
description In this paper, we continue our study of closed models defined in categories of graphs. We construct a closed model defined in the cat-egory of directed graphs which characterizes the strongly connected components. This last notion has many applications, and it plays an important role in the web search algorithm of Brin and Page, the foun-dation of the search engine Google. We also show that for this closed model, Euler graphs are particular examples of cofibrant objects. This enables us to interpret in this setting the classical result of Euler which states that a directed graph is Euleurian if and only if the in degree and the out degree of every of its nodes are equal. We also provide a cohomological proof of this last result.
author Aristide,Tsemo
spellingShingle Aristide,Tsemo
Closed models, strongly connected components and Euler graphs
author_facet Aristide,Tsemo
author_sort Aristide,Tsemo
title Closed models, strongly connected components and Euler graphs
title_short Closed models, strongly connected components and Euler graphs
title_full Closed models, strongly connected components and Euler graphs
title_fullStr Closed models, strongly connected components and Euler graphs
title_full_unstemmed Closed models, strongly connected components and Euler graphs
title_sort closed models, strongly connected components and euler graphs
publisher Universidad Católica del Norte, Departamento de Matemáticas
publishDate 2016
url http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0716-09172016000200001
work_keys_str_mv AT aristidetsemo closedmodelsstronglyconnectedcomponentsandeulergraphs
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