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Mathematics   > Home   > Advances in Pure and Applied Mathematics   > Issue 4 (September 2024)   > Article

Morphology of the connected components of the boolean sum of two digraphs (≤ 5)-hypomorphic up to complementation

Forme des composantes connexes de la somme booléenne de deux digraphes (≤ 5)-hypomorphes à complémentaire près


Aymen Ben Amira
Faculty of Sciences of Sfax
Tunisia

Jamel Dammak
Faculty of Sciences of Sfax
Tunisia

Hamza Si Kaddour
Université Claude Bernard Lyon 1
France



Published on 18 September 2024   DOI : 10.21494/ISTE.OP.2024.1198

Abstract

Résumé

Keywords

Mots-clés

Let $$$G=(V,E)$$$ and $$$G'=(V,E')$$$ be two digraphs, $$$(\leq 5)$$$-hypomorphic up to complementation, and $$$U:=G\dot{+} G'$$$ be the boolean sum of $$$G$$$ and $$$G'$$$. The case where $$$U$$$ and $$$\overline U$$$ are both connected was studied by the authors and B.Chaari giving the form of the pair$$$\{G, G'\}$$$. In this paper we study the case where $$$U$$$ is not connected and give the morphology of the pair $$$\{G_{\restriction {V({\mathcal C})}},G'_{\restriction {V({\mathcal C})}}\}$$$ whenever $$$C$$$ is a connected component of $$$U$$$.

Let $$$G=(V,E)$$$ and $$$G'=(V,E')$$$ be two digraphs, $$$(\leq 5)$$$-hypomorphic up to complementation, and $$$U:=G\dot{+} G'$$$ be the boolean sum of $$$G$$$ and $$$G'$$$. The case where $$$U$$$ and $$$\overline U$$$ are both connected was studied by the authors and B.Chaari giving the form of the pair$$$\{G, G'\}$$$. In this paper we study the case where $$$U$$$ is not connected and give the morphology of the pair $$$\{G_{\restriction {V({\mathcal C})}},G'_{\restriction {V({\mathcal C})}}\}$$$ whenever $$$C$$$ is a connected component of $$$U$$$.

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