Enumeration of connected components of acyclic digraph. (3rd October 2021)

• Record Type: Journal Article
• Authors: Al'Dzhabri, Kh. Sh.
• Is Part Of: Journal of discrete mathematical sciences & cryptography. Volume 24:Number 7(2021)
• Page Start: 2047
• Page End: 2058
• Publication Date: 2021-10-03
• Subjects: 05C30; Graph -- Binary relation -- Acyclic digraphs; Computer science -- Mathematics -- Periodicals; Cryptography -- Periodicals; Computer science -- Mathematics; Cryptography; Periodicals; 004.0151
• DOI: 10.1080/09720529.2021.1965299
• Languages: English
• ISSNs: 0972-0529

Abstract

Abstract: We established the concept of a binary reflexive relation of adjacency and determined the algebraic system consisting of all binary relations of set X and all unordered pairs of binary relations in terms of characteristic functions on the set of all binary relations of the set X . We investigated some properties of algebraic system of the structure of acyclic digraph. Also, we prove that if σ and τ are adjacent relations, then σ is acyclic relation (finite acyclic digraph) if and only if τ is an acyclic relation. Finally, the number of connected components of an acyclic relations graph is given an exact formula.