https://dspace.univ-ouargla.dz/jspui/handle/123456789/1550 Sat, 02 May 2026 05:04:34 GMT 2026-05-02T05:04:34Z https://dspace.univ-ouargla.dz/jspui/handle/123456789/12043 Titre: Le nombre de domination par contraction Auteur(s): Kamel, Tablennehas; Mustapha, Chellali Résumé: RØsumØ Soit G = (V;E) un graphe simple. Un sous-ensemble S de V est un dominant de G si tout sommet de V S est adjacent à au moins un sommet de S. Le cardinal minimum d un ensemble dominant de G, notØ (G), est appelØ nombre de domination. Un ensemble dominant stable d un graphe G est un ensemble dominant dont le sous-graphe induit est un stable. Le cardinal minimum d un ensemble dominant stable de G, notØ i(G), est appelØ nombre de domination stable. Etant donnØ un paramŁtre de domination d un graphe G, on dØ ni le nombre de domination par contraction d un graphe G connexe, notØ Ct (G) comme Øtant le nombre minimum d arŒtes à contracter successivement pour faire diminuer le nombre de domination (G): Dans [4] Huang et Jun-Ming ont montrØs que Ct (G) 3 pour tout graphe G: Dans ce papier, On donne une rØponse au problŁme posØ par Huang et Jun-Ming dans l article [4], en caractØrisant les arbres T ayant Ct (T) = 3: Ensuite, on montre qu il existe des graphes oø le nombre de domination stable par contraction est trŁs grand. Mon, 07 Nov 2016 00:00:00 GMT https://dspace.univ-ouargla.dz/jspui/handle/123456789/12043 2016-11-07T00:00:00Z https://dspace.univ-ouargla.dz/jspui/handle/123456789/12041 Titre: Bounds on the domination number in oriented graphs Auteur(s): Mostafa, Blidia; Lyes, Ould-Rabah Résumé: Abstract A dominating set of an oriented graph D is a set S of vertices of D such that every vertex not in S is a successor of some vertex of S. The minimum cardinality of a dominating set of D; denoted (D), is the domination number of D. An irredundant set of an oriented graph D is a set S of vertices of D such that every vertex of S has a private successor, that is, for all x 2 S; jO[x] O[S x]j 1. The irredundance number of an oriented graph, denoted ir(D), is the least number of vertices in a maximal irredundant set. We denote by (D) and s(D); the number of edges in a maximum matching and support vertices of the underlyng graph of an oriented graph D; respectively. In this paper, we show that for every oriented graph D, s(D) ir(D) (D) 6 n(D) 1 (D). We also give characterizations of oriented trees satisfying (T) = n(T) (T) and oriented graphs satisfying (D) = s(D) and s(D) = n(D) (D); respectively. Mon, 07 Nov 2016 00:00:00 GMT https://dspace.univ-ouargla.dz/jspui/handle/123456789/12041 2016-11-07T00:00:00Z https://dspace.univ-ouargla.dz/jspui/handle/123456789/12039 Titre: Note on b-colorings in Harary graphs Auteur(s): Zoham, Zemir; Noureddine, Ikhlef; Eschouf, z Résumé: Abstract A b-coloring is a coloring of the vertices of a graph such that each color class contains a vertex that has a neighbor in all other color classes. The b-chromatic number b(G) is the largest integer k such that G admits a b-coloring with k colors. In this note, according to the values taken by the order n of a graph, we determine exact values or bounds for the b-chromatic number of H 2m;n which is the Harary graph H when k is even: Therefore our result improves the result concerning the b-chromatic of p-th power graphs of cycles and give a negative answer to the open problem of E⁄antin and Kheddouci. k;n Mon, 07 Nov 2016 00:00:00 GMT https://dspace.univ-ouargla.dz/jspui/handle/123456789/12039 2016-11-07T00:00:00Z https://dspace.univ-ouargla.dz/jspui/handle/123456789/12038 Titre: Double domination edge removal critical graphs Auteur(s): Mostafa, Blidia; Mustapha, Chellali; Sou ane, Kheli Résumé: Abstract Let G be a graph without isolated vertices: A set S V (G) is a double dominating set if every vertex in V (G) is adjacent to at least two vertices in S. G is said edge removal critical graph with respect to double domination, if the removal of any edge increases the double domination number. In this paper, we rst give a necessary and su¢ cient conditions for -critical graphs. Then we provide a constructive characterization of critical trees. Mon, 07 Nov 2016 00:00:00 GMT https://dspace.univ-ouargla.dz/jspui/handle/123456789/12038 2016-11-07T00:00:00Z