Hyperoperations on directed graphs

Kalampakas, Antonios; Spartalis, Stefanos

doi:10.47974/JDMSC-1714

Open Access Research Article

Hyperoperations on directed graphs

^*Antonios KalampakasCorresponding authorantonios.kalampakas@aum.edu.kwCollege of Engineering and Technology American University of the Middle EastEgaila, 54200, KuwaitView full profile → , Stefanos Spartalissspart@pme.duth.gr, spartalis.stefanos@ac.eap.grDepartment of Production and Management Engineering Laboratory of Computational Mathematics, School of Engineering, Democritus University of Thrace V.Sofias 12, Prokat; Hellenic Open University School of Science and Technology Studies in Physics 18 Aristoteles by streetDepartment of Production and Management Engineering Laboratory of Computational Mathematics, School of Engineering, Democritus University of Thrace V.Sofias 12, ProkatBuilding A1, Xanthi, 67132, GreeceView full profile →

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pp. 1011–1025Vol. 27Issue 3April 2024DOI: 10.47974/JDMSC-1714 Crossmark XML

Received:: 03 Feb 2022
Accepted:: 05 Jul 2022
Published Online:: 01 May 2024
Article type:: Research Article
Language:: EN
Article no.:: JDMSC-1714
Pages:: 1011–1025

Abstract

We analyze three hyper-operations derived from directed graphs, demonstrate the influence of the underlying graph structure on these hyper-operations and study the algebraic properties of the related classes of graphs. The paper also illustrates the relationship between directed graphs and hyper-structures using graph hyper-operations. In addition, we investigate the property of commutativity for an appropriate type of hyper-groupoids and its relationship to properties of directed graphs. Therefore, the paper consists of three sections, section one introduces and investigates three distinct hyper-groupoids derived from hyper-operations on directed graphs, section two discusses the fundamental ideas of directed graphs, and section three elaborates on path, simple path, and ancestry hyper-operations.

Keywords

Binary relation Hyper-groupoids Directed graphs Path hyper-operations C-hyper-groupoid

Subject Classifications

(2010) 05C2020N2005C38

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