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Keywords = network quasi-semilattices

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15 pages, 344 KiB  
Article
Quasi-Semilattices on Networks
by Yanhui Wang and Dazhi Meng
Axioms 2023, 12(10), 943; https://doi.org/10.3390/axioms12100943 - 30 Sep 2023
Cited by 4 | Viewed by 1948
Abstract
This paper introduces a representation of subnetworks of a network Γ consisting of a set of vertices and a set of relations, where relations are the primitive structures of a network. It is proven that all connected subnetworks of a network Γ form [...] Read more.
This paper introduces a representation of subnetworks of a network Γ consisting of a set of vertices and a set of relations, where relations are the primitive structures of a network. It is proven that all connected subnetworks of a network Γ form a quasi-semilattice L(Γ), namely a network quasi-semilattice.Two equivalences σ and δ are defined on L(Γ). Each δ class forms a semilattice and also has an order structure with the maximum element and minimum elements. Here, the minimum elements correspond to spanning trees in graph theory. Finally, we show how graph inverse semigroups, Leavitt path algebras and Cuntz–Krieger graph C*-algebras are constructed in terms of relations. Full article
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