@ARTICLE{10.21494/ISTE.OP.2024.1198, 

TITLE={Morphology of the connected components of the boolean sum of two digraphs (≤ 5)-hypomorphic up to complementation}, 
  
AUTHOR={Aymen Ben Amira
, Jamel Dammak 
, Hamza Si Kaddour, }, 
	
JOURNAL={Advances in Pure and Applied Mathematics}, 
	
VOLUME={15}, 

NUMBER={Issue 4 (September 2024)}, 
	
YEAR={2024}, 

URL={https://www.openscience.fr/Morphology-of-the-connected-components-of-the-boolean-sum-of-two-digraphs-5}, 
	
DOI={10.21494/ISTE.OP.2024.1198}, 
	
ISSN={1869-6090}, 
	
ABSTRACT={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 $$$U$$$.}}