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2009 A homotopical algebra of graphs related to zeta series
Terrence Bisson, Aristide Tsemo
Homology Homotopy Appl. 11(1): 171-184 (2009).


The purpose of this paper is to develop a homotopical algebra for graphs, relevant to the zeta series and the spectra of finite graphs. More precisely, we define a Quillen model structure in a category of graphs (directed and possibly infinite, with loops and multiple arcs allowed). The weak equivalences for this model structure are the Acyclics (graph morphisms which preserve cycles). The cofibrations and fibrations for the model are determined from the class of Whiskerings (graph morphisms produced by grafting trees). Our model structure seems to fit well with the importance of acyclic directed graphs in many applications.


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Terrence Bisson. Aristide Tsemo. "A homotopical algebra of graphs related to zeta series." Homology Homotopy Appl. 11 (1) 171 - 184, 2009.


Published: 2009
First available in Project Euclid: 1 September 2009

zbMATH: 1186.05062
MathSciNet: MR2506131

Primary: 05C20‎ , 18G55 , 55U35

Keywords: Category of directed graphs , cycles , Quillen model structure , topos , weak factorization system , zeta function

Rights: Copyright © 2009 International Press of Boston

Vol.11 • No. 1 • 2009
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