Digraph constructions based on inverter subsets in EQ-algebras

Articles in Press

Document Type : Research Paper

Authors

1 Payame Noor University

2 Payame Noor Unoversity, Iran, Tehran

Abstract

This paper introduces the notions of (meet, extended, symmetrical) EQ-algebras and valued indicator subsets within this framework. We present a new class of EQ-algebras and prove that every finite chain and countable set can be structured as an extended EQ-algebra. A primary contribution is establishing a connection between the class of digraphs and the class of EQ-algebras. To this end, we define the concepts of inverter digraphs and valued indicator digraphs based on EQ-algebras, which are founded on the corresponding notions of inverter subsets and valued indicator subsets. We investigate the relationship between these two types of digraphs, providing conditions under which they are isomorphic and showing that valued indicator digraphs are spanning subgraphs of inverter digraphs under certain constraints. Finally, leveraging this correspondence, we demonstrate a method to extract EQ-algebras from (weakly) strong digraphs.

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References

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Journal of Hyperstructures

Articles in Press, Accepted Manuscript
Available Online from 17 June 2026

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