DSpace Collection:
https://dspace.univ-ouargla.dz/jspui/handle/123456789/1550
2024-03-29T15:12:49ZLe nombre de domination par contraction
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.2016-11-07T00:00:00ZBounds on the domination number in oriented graphs
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.2016-11-07T00:00:00ZNote on b-colorings in Harary graphs
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;n2016-11-07T00:00:00ZDouble domination edge removal critical graphs
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.2016-11-07T00:00:00Z