A homotopical algebra of graphs related to zeta series

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dc.creatorBisson, Terrence
dc.creatorTsemo, Aristide
dc.date2008-02-26
dc.date.accessioned2026-07-07T09:23:21Z
dc.date.available2026-07-07T09:23:21Z
dc.descriptionThe purpose of this paper is to develop a homotopical algebra for graphs, relevant to zeta series and 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. In addition to the weak factorization systems which form this model structure, we also describe two Freyd-Kelly factorization systems based on Folding, Injecting, and Covering graph morphisms.
dc.identifierhttps://arxiv.org/abs/0802.3859
dc.identifierhttp://arxiv.org/abs/0802.3859
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/155702
dc.subjectCombinatorics
dc.subjectAlgebraic Topology
dc.subject05C20, 55U35
dc.titleA homotopical algebra of graphs related to zeta series
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