Distinguishing Number for some Circulant Graphs

Introduced by Albertson et al. \cite{albertson}, the distinguishing number $D(G)$ of a graph $G$ is the least integer $r$ such that there is a $r$-labeling of the vertices of $G$ that is not preserved by any nontrivial automorphism of $G$. Most of graphs studied in literature have 2 as a distinguishing number value except complete, multipartite graphs or cartesian product of complete graphs depending on $n$. In this paper, we study circulant graphs of order $n$ where the adjacency is defined using a symmetric subset $A$ of $\mathbb{Z}_n$, called generator. We give a construction of a family of circulant graphs of order $n$ and we show that this class has distinct distinguishing numbers and these lasters are not depending on $n$

A New Game Invariant of Graphs: the Game Distinguishing Number

The distinguishing number of a graph $G$ is a symmetry related graph invariant whose study started two decades ago. The distinguishing number $D(G)$ is the least integer $d$ such that $G$ has a $d$-distinguishing coloring. A distinguishing $d$-coloring is a coloring $c:V(G)\rightarrow\{1,...,d\}$ invariant only under the trivial automorphism. In this paper, we introduce a game variant of the distinguishing number. The distinguishing game is a game with two players, the Gentle and the Rascal, with antagonist goals. This game is played on a graph $G$ with a set of $d\in\mathbb N^*$ colors. Alternately, the two players choose a vertex of $G$ and color it with one of the $d$ colors. The game ends when all the vertices have been colored. Then the Gentle wins if the coloring is distinguishing and the Rascal wins otherwise. This game leads to define two new invariants for a graph $G$, which are the minimum numbers of colors needed to ensure that the Gentle has a winning strategy, depending on who starts. These invariants could be infinite, thus we start by giving sufficient conditions to have infinite game distinguishing numbers. We also show that for graphs with cyclic automorphisms group of prime odd order, both game invariants are finite. After that, we define a class of graphs, the involutive graphs, for which the game distinguishing number can be quadratically bounded above by the classical distinguishing number. The definition of this class is closely related to imprimitive actions whose blocks have size $2$. Then, we apply results on involutive graphs to compute the exact value of these invariants for hypercubes and even cycles. Finally, we study odd cycles, for which we are able to compute the exact value when their order is not prime. In the prime order case, we give an upper bound of $3$

Tourism impact on the social development in Algeria

The social effects in host communities resulted from the direct and indirect relationship with tourists, thus dealing with the tourism industry. For multiple reasons host communities are the weakest in their coping with the guests, and service providing. The negative effects arise when tourism brings changes to the values and behaviours systems, it threatens the national identity, as well as the changes occurrence in social structures, family relations, traditional collective ways of life and morality. Tourism positive social impacts are represented in: the cultural exchange between the citizen and tourists, the increase of economic level and civilization, the revival of local architectural traditions, to raise the psychological health level of the society and to encourage the arts and local industries. The development of responsible tourism may contribute to the eradication of poverty, which is one of the millennium goals for development since "the tourism sector is a source of growth and development. Hence we can ask the following question: What are the impacts of tourism promotion on the social development in Algeria? Keywords: Tourism, Sustainable Tourism, Development, Social Development, Poverty, Algeria

The Impact of Incentives on Productivity in Mobilis “Algerie Telecom”

To realize the objectives of this paper , a survey study was administered at mobilis. According to the results of the study, most of the employees think that the level of utilization of the non-financial incentives in their organization is inadequate. Also, the findings suggest that they value non-financial incentives as much as financial incentives. Thus, within the limitations of the survey study, it may be concluded that non-financial incentives have the potential to increase the motivation of personnel in mobilis Keywords: Motivation, training, productivity, financial incentives, non financial incentives. job satisfactio

The Role of Intellectual Capital in the Development of Business Organizations: A Case Study of the IBM

The Intellectual capital is a contemporary topics, which focuses on energy innovation and creativity in when working in the organization, is the latest production which recognized as a key resource to create wealth and that his agents (intellectual capital) role in the prosperity of organizations as a result regarded as a competitive advantage and great wealth and factor the survival of her, making intellectual capital management an urgent demand in light of the Organization's presence in an environment of rapidly change.We came through this research that intellectual capital is the essential foundation for the construction of economic progress in general excellence and organizations in particular. Key words: intellectual capital, human capital, modern organizations, knowledge management, IBM Corporation

Optimizing polymer-stabilized raw earth composite with plant fibers reinforcement for historic building rehabilitation

This research focuses on the optimization of formulation, characterization, and damage analysis of plant fiber-reinforced polyester resin composites (jute and date palm). To better understand the characteristics and mechanical behavior of these materials, this study investigates the influence of resin content and plant fibers on the physico-mechanical behavior of the resin composites. Resinous composites consisting of polyester resin and raw earth were studied using a novel formulation based on an empirical method that follows the principle of earth saturation with polyester resin. Saturation was achieved with a 28% content of polyester resin, which appeared to be an optimal blend for the earth–resin composite. Plant fibers were randomly incorporated as reinforcement in the composites at various percentages (1%, 2%, and 3%) and lengths (0.5 cm, 1 cm, and 1.5 cm). Mechanical tests including bending, compression, and indentation were conducted to evaluate the mechanical properties of the composites. Analysis of fracture morphology revealed that the deformation and rupture mechanisms in bending, compression, and indentation of these composites differ from those of traditional concrete and cement mortar. The obtained results indicate that the composites exhibit acceptable performance and could be favorably employed in the rehabilitation of historic buildings