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1

Investigation, analysis and comparison of current-voltage characteristics for Au/Ni/GaN Schottky structure using I-V-T simulation

Sadoun A., Mansouri S., Chellali M., Lakhdar N., Hima A., Benamara Z.

Materials Science Poland

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2019

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Vol. 37, No. 3

496--502

EN

In this work, we have presented a theoretical study of Au/Ni/GaN Schottky diode based on current-voltage (I-V) measurement for temperature range of 120 K to 400 K. The electrical parameters of Au/Ni/GaN, such as barrier height (Φb), ideality factor and series resistance have been calculated employing the conventional current-voltage (I-V), Cheung and Chattopadhyay method. Also, the variation of Gaussian distribution (P (Φb)) as a function of barrier height (Φb) has been studied. Therefore, the modified [formula] relation has been extracted from (I-V) characteristics, where the values of ΦB0 and A+Simul have been found in different temperature ranges. The obtained results have been compared to the existing experimental data and a good agreement was found.

2

A note on k-Roman graphs

Bouchou A., Blidia M., Chellali M.

Opuscula Mathematica

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2013

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Vol. 33, no. 4

641--646

EN

Let G = (V,E) be a graph and let k be a positive integer. A subset D of V (G) is a k-dominating set of G if every vertex in V (G) \D has at least k neighbours in D. The k-domination number Υk(G) is the minimum cardinality of a k-dominating set of G. A Roman k-dominating function on G is a function f : V (G) →{0, 1, 2} such that every vertex u for which f(u) = 0 is adjacent to at least k vertices v1, v2, . . . , vk with f(vi) = 2 for i = 1, 2, . . . , k. The weight of a Roman k-dominating function is the value [formula] and the minimum weight of a Roman k-dominating function on G is called the Roman k-domination number Υk(G) of G. A graph G is said to be a k-Roman graph if ΥkR(G) = 2Υk(G) . In this note we study k-Roman graphs.

3

Global offensive k-alliance in bipartite graphs

Chellali M., Volkmann L.

Opuscula Mathematica

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2012

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Vol. 32, no. 1

83-89

EN

Let k ≥ 0 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if /N(v) ∩ S/ ≥ /N(v) - S/ + k for every v ∈ V (G) - S, where 0 ≤ k Δ and Δ is the maximum degree of G. The global offensive k-alliance number [formula] is the minimum cardinality of a global offensive k-alliance in G. We show that for every bipartite graph G and every integer k ≥ 2, [formula], where Lk(G) is the set of vertices of degree at most k - 1. Moreover, extremal trees attaining this upper bound are characterized.

4

A note on the independent Roman domination in unicyclic graphs

Chellali M., Rad N. J.

Opuscula Mathematica

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2012

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Vol. 32, no. 4

715-718

EN

A Roman dominating function (RDF) on a graph G= (V, E) is a function ƒ : V → {0, 1, 2} satisfying the condition that every vertex u for which ƒ(u) = 0 is adjacent to at least one vertex v for which ƒ(v)=2. The weight of an RDF is the value [formula]. An RDF ƒ in a graph G is independent if no two vertices assigned positive values are adjacent. The Roman domination number ΥR (G) (respectively, the independent Roman domination number ΥR(G) is the minimum weight of an RDF (respectively, independent RDF) on G. We say that ΥR(G) strongly equals iR(G), denoted by ΥR(G) ≡ iR(G), if every RDF on G of minimum weight is independent. In this note we characterize all unicyclic graphs G with ΥR(G) ≡ iR(G).

5

A note on a relation between the weak and strong domination numbers of a graph

Boutrig R., Chellali M.

Opuscula Mathematica

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2012

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Vol. 32, no. 2

235-238

EN

In a graph G = (V, E) a vertex is said to dominate itself and all its neighbors. A set D ⊆ V is a weak (strong, respectively) dominating set of G if every vertex v ∈ V - S is adjacent to a vertex u ∈ D such that dG(v) ≥ dG(u) (dG(v) ≤ dG(u), respectively). The weak (strong, respectively) domination number of G, denoted by ϒw(G) (ϒs(G), respectively), is the minimum cardinality of a weak (strong, respectively) dominating set of G. In this note we show that if G is a connected graph of order n ≥ 3, then ϒw(G) + tϒs(G) ≤ n, where t = 3/(Δ+1) if G is an arbitrary graph, t = 3/5 if G is a block graph, and t = 2/3 if G is a claw free graph.

6

A note on global alliances in trees

Bouzefrane M., Chellali M.

Opuscula Mathematica

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2011

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Vol. 31, no. 2

153-159

EN

For a graph G = (V,E), a set S ⊆ V is a dominating set if every vertex in V - S has at least a neighbor in S. A dominating set S is a global offensive (respectively, defensive) alliance if for each vertex in V - S (respectively, in S) at least half the vertices from the closed neighborhood of v are in S. The domination number γ (G) is the minimum cardinality of a dominating set of G, and the global offensive alliance number γo(G) (respectively, global defensive alliance number γa(G)) is the minimum cardinality of a global offensive alliance (respectively, global deffensive alliance) of G. We show that if T is a tree of order n, then γo(T) ≤ 2γ (T) - 1 and if n ≥ 3, then γo(T) ≤ 3/2?a(T) ? 1. Moreover, all extremal trees attaining the first bound are characterized.

7

Trees with equal global offensive k-alliance and k-domination numbers

Chellali M.

Opuscula Mathematica

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2010

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Vol. 30, no. 3

249-254

EN

Let k ≥ 1 be an integer. A set S of vertices of a graph G = (V (G), E(G)) is called a global offensive k-alliance if |N(v) ∩ S| ≥ |N(v) - S| + k for every v ∈ V (G) - S, where N(v) is the neighborhood of v. The subset S is a k-dominating set of G if every vertex in V (G) - S has at least k neighbors in S. The global offensive k-alliance number [formula] is the minimum cardinality of a global offensive k-alliance in G and the k-domination number ϒ k(G) is the minimum cardinality of a k-dominating set of G. For every integer k ≥ 1 every graph G satisfies [formula]. In this paper we provide for k ≥ 2 a characterization of trees T with equal [formula] and ϒ k(T).

8

On the global offensive alliance number of a tree

Bouzefrane M., Chellali M.

Opuscula Mathematica

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2009

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Vol. 29, no. 3

223-228

EN

For a graph G = (V, E), a set S ⊆ V is a dominating set if every vertex in V - S has at least a neighbor in S. A dominating set S is a global offensive alliance if for every vertex v in V - S, at least half of the vertices in its closed neighborhood are in S. The domination number ϒ(G) is the minimum cardinality of a dominating set of G and the global offensive alliance number ϒo(G) is the minimum cardinality of a global offensive alliance of G. We first show that every tree of order at least three with l leaves and s support vertices satisfies ϒo(T) ≥ (n - l + s + 1)/3 and we characterize extremal trees attaining this lower bound. Then we give a constructive characterization of trees with equal domination and global offensive alliance numbers.

9

A note on Vizing's generalized conjecture

Blidia M., Chellali M.

Opuscula Mathematica

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2007

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Vol. 27, no. 2

181-185

EN

In this note we give a generalized version of Vizing's conjecture concerning the distance domination number for the cartesian product of two graphs.

10

Bounds on the 2-domination number in cactus graphs

Chellali M.

Opuscula Mathematica

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2006

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Vol. 26, no. 1

5-12

EN

A 2-dominating set of a graph G is a set D of vertices of G such that every vertex not in S is dominated at least twice. The minimum cardinality of a 2-dominating set of G is the 2-domination number γ2(G). We show that if G is a nontrivial connected cactus graph with k(G) even cycles (k(G) ≥ 0), then γ2(G) ≥ γt(G) - k(G), and if G is a graph of order n with at most one cycle, then γ2(G) ≥ (n + l - s)/2 improving Fink and Jacobson's lower bound for trees with l > s, where γt(G), l and s are the total domination number, the number of leaves and support vertices of G, respectively. We also show that if T is a tree of order n ≥ 3, then γ2(T) ≤ β(T) + s - 1, where β(T) is the independence number of T.