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Coverings of graphoids [Elektronski vir] : existence theorem and decomposition theoremsMalnič, Aleksander ; Zgrablić, BorisA graphoid is a mixed multigraph with multiple directed and/or undirected edges, loops, and semiedges. A covering projection of graphoids is an onto mapping between two graphoids such that at each ... vertex, the mapping restricts to a local bijection on incoming edges and outgoing edges. Naturally, as it appears, this definition displays unusual behaviour since the projection of the corresponding underlying graphs is not necessarily a graph covering. Yet, it is still possible to grasp such coverings algebraically in terms of the action of the fundamental monoid and combinatorially in terms of voltage assignments on arcs. In the present paper, the existence theorem is formulated and proved in terms of the action of the fundamental monoid. A more conventional formulation in terms of the weak fundamental group is possible because the action of the fundamental monoid is permutational. The standard formulation in terms of the fundamental group holds for a restricted class of coverings, called homogeneous. Further, the existence of the universal covering and the problems related to decomposing regular coverings via regular coverings are studied in detail. It is shown that with mild adjustments in the formulation, all the analogous theorems that hold in the context of graphs are still valid in this wider setting.Source: Symmetry [Elektronski vir]. - ISSN 2073-8994 (Vol. 16, iss. 3, art. 375, 2024, str. 1-22)Type of material - e-article ; adult, seriousPublish date - 2024Language - englishCOBISS.SI-ID - 195093251
Author
Malnič, Aleksander |
Zgrablić, Boris
Topics
mixed-graph graphoid |
covering projection |
voltage action |
homotopy |
monoid action |
lifting automorphisms
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Malnič, Aleksander | 02507 |
Zgrablić, Boris | 11687 |
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