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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

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Let G=(V,E) and G=(V,E) be two digraphs, (5)-hypomorphic up to complementation, and U:=G˙+G be the boolean sum of G and G. The case where U and ¯¯¯¯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 {GV(C),GV(C)} whenever C is a connected component of U.

Let G=(V,E) and G=(V,E) be two digraphs, (5)-hypomorphic up to complementation, and U:=G˙+G be the boolean sum of G and G. The case where U and ¯¯¯¯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 {GV(C),GV(C)} whenever C is a connected component of U.

Digraph graph isomorphism k-hypomorphy up to complementation boolean sum tournament interval

Digraph graph isomorphism k-hypomorphy up to complementation boolean sum tournament interval

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