Let $G=(V, E)$ be a simple graph. A dominating set of $G$ is a subset $D\subseteq V$ such that every vertex not in $D$ is adjacent to at least one vertex in $D$. The cardinality of the smallest dominating set of $G$, denoted by $\gamma(G)$, is the domination number of $G$. For $k \geq 1$, a $k$-fair dominating set ($kFD$-set) in $G$, is a dominating set $S$ such that $|N(v) \cap D|=k$ for every vertex $ v \in V\setminus D$. A fair dominating set in $G$ is a $kFD$-set for some integer $k\geq 1$. Let ${\cal D}_f(G,i)$ be the family of the fair dominating sets of a graph $G$ with cardinality $i$ and let $d_f(G,i)=|{\cal D}_f(G,i)|$. The fair domination polynomial of $G$ is $D_f(G,x)=\sum_{ i=1}^{|V(G)|} d_f(G,i) x^{i}$. In this paper, after computation of the fair domination number of power of cycle, we count the number of the fair dominating sets of certain graphs such as cubic graphs of order~$10$, power of paths, and power of cycles. As a consequence, all cubic graphs of order $10$ and especially the Petersen graph are determined uniquely by their fair domination polynomial.

We revised our technique for generating graphical renderings of the limitsets of Kleinian groups. The algorithm, relying on numerical base conversion,has been improved to shorten computation times. This method easily applies toany family of Kleinian groups with an arbitrary number of generators.Following an overview of this problem, we present the implementationguidelines in the form of pseudo-code.

One important criterion in decision-making when we want to purchase a product or a service is users’ reviews. When something is valuable, it’s fake and will be created as well. It is the same for users’ reviews. The purpose of these fake reviews is to deceive users, leading them to make a wrong choice. One challenging problem is when we can trust a review. Although many researchers attempted to address this problem, none of them pictured the problem in a streaming domain. With the help of the review network’s properties, we propose a model to find reliable reviews when reviews are coming in a stream. Our model is fast and online, that is, it is capable of identifying reliable reviews as they are been submitted, and scalable because it is a complementary model to offline models in detecting fake reviews.

In this paper, we consider only finite, undirected, and simple graphs. The concept of cordial labeling was introduced by Cahit[4]. Different types of cordial-related labeling were studied in [1, 2, 3, 5, 16]. In a similar line, the notion of pair difference cordial labeling of a graph was introduced in [8]. The pair difference cordial labeling behavior of several graphs like path, cycle, star, wheel, triangular snake, alternate triangular snake, butterfly, ladder, Mobius ladder, slanting ladder, and union of some graphs have been investigated in [ 8, 9, 10, 11, 12, 13, 14, 15]. The $m-$ copies of a graph $G$ is denoted by $mG$ [7]. In this paper, we investigate the pair difference cordial labeling behavior of $m-$ copies of Path, Star, Cycle, and Ladder graphs.

The selection of features is a crucial step in the analysis of high-dimensional data in machine learning and data mining. Gannet Optimization Algorithm (GOA) is a recently proposed metaheuristic algorithm that has not yet been investigated in terms of its capacity to solve feature selection problems. A new wrapper feature selection approach based on GOA is proposed to extract the best features. The GOA is a robust meta-heuristic algorithm that can deal with higher dimensions. A fitness function is used to account for the entropy of the sensitivity and specificity, as well as the accuracy of the classifier and the fraction of features selected. Additionally, four new algorithms are compared with the proposed algorithm in this paper. Based on the experimental results, fewer features can be obtained with a higher classification accuracy using the proposed algorithm.

Artificial neural networks that have been so popular in recent years, are inspired from biological neural networks in the nature. The aim of this work is to study the properties of biological neural networks to find out what is actually happening in these networks. To do so, we study on Caenrohibditis elegans neural network, which is the simplest and the only biological neural network that is fully mapped. We implemented the sub-circuit of C.elegans neural network that is associated with the sensation of aversive stimuli which results in forward and backward locomotion, and we found out that some of its neurons are ineffective in developing considered outputs. However, removing these neurons together has considerable effect on these outputs.

In this article, we examine different algorithms in the field of cryptography. And we analyze them from different aspects. Also, we introduce a new solution and algorithm, based on increasing data security. Our proposed method can perform the task optimally and efficiently compared to similar algorithms. In addition, it also reduces the need for storage space. Therefore, our proposed method works better and optimally by increasing productivity in operational environments. Our proposed algorithm can be used by increasing the security level for data, in various platforms and in all types of communication. Because the data is linked, and if we do not have the address of a data packet, it is not possible to decode the data. This increases data security.

Entropy is a measure of disorder in a system and is widely used in other scientific and engineering disciplines such as statistical mechanics and information theory. In a chaotic supply chain, the goal is to reduce chaotic behaviors and predict the future of the supply chain. In this case, relationships in a three-tier supply chain are considered in a continuous-time environment. In this paper, the chaotic supply chain is investigated and controlled using the entropy minimization method. Due to the dynamic nature of the supply chain and its chaotic behavior, Poincaré mapping of the system has been prepared by the stroboscopic method. Then, by defining Shannon entropy on the map, the entropy of the system is significantly reduced by the gradient descent algorithm.