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

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


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



Validé le 21 mai 2024   DOI : À venir

Résumé

Abstract

Mots-clés

Keywords

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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