569 KB91 KB200820252025Malnič, AleksanderZgrablić, Borisletnik:25številka:3str. 1-29DOI:10.26493/1855-3974.3267.7d4ISSN:1855-3966COBISSID_HOST:200176899URN:URN:NBN:SI:doc-OQ9HNV52enUniverza na Primorskem, Fakulteta za matematiko, naravoslovje in informacijske tehnologijeArs mathematica contemporaneacovering projectiondartgeneral digraphhomotopylifting automorphismsmixed graphmonoid actionvoltageCoverings of general digraphs|A unified theory of covering projections of graphs and digraphs is presented as one theory by considering coverings of general digraphs, where multiple directed and undirected edges together with oriented and unoriented loops and semiedges, are allowed. It transpires that coverings of general digraphs can display certain pathological behaviour since the naturally defined projections of their underlying graphs may not be coverings in the usual topological sense. Consequently, homotopy does not always lift, although the unique walk lifting property still holds. Yet, it is still possible to grasp such coverings algebraically in terms of the action of the fundamental monoid. This action is permutational and has certain nice properties that monoid actions in general do not have. As a consequence, such projections can be studied combinatorially in terms of voltages. The problem of isomorphism and equivalence, and in particular, the problem of lifting automorphisms, is treated in depth. All known results about covering projections of graphs are simple corollaries of just three general theoremsTEXTznanstveno časopisjejournalsSlovenian National E-content AggregatorNational and University Library of SloveniaUniverza na Primorskem, Fakulteta za naravoslovje, matematiko in informacijske tehnologije