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

## [FORTHCOMING] 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

Université Claude Bernard Lyon 1
France

Validated on 21 May 2024   DOI : TBA

### 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 $U$.