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For given integer e and q, let p(e, q) (res. C(e, q)) indicate to (MDe-PD). The maximum diameter deleting e edges from a connected graph of diameter q is f(e, q), the maximum number TF(f, q) of edg...

Data security is an important component of data communication and transmission systems. Its main role is to keep sensitive information safe and integrated from the sender to the receiver. The proposed system aims to secure text messages through two security principles encryption and steganography. The system produced a novel method for encryption using graph theory properties; it formed a graph from a password to generate an encryption key as a weight matrix of that graph and invested the Least Significant Bit (LSB) method for hiding the encrypted message in a colored image within a green component. Practical experiments of (perceptibility, capacity, and robustness) were calculated using similarity measures like PSNR, MSE, and SSIM. These measures had proved the efficiency of the system for image quality and hiding messages with PSNR ratio more than 85 dB, MSE ranged (4.537e-05 to 5.27546e-04) and SSIM=1.0 for using a cover file with size ranged from 256×300 to 1200×760 pixels and message ranged from 16 to 300 characters.

The intuitionistic fuzzification in ρ-algebras about the concepts of ideals and subalgebras given with several related characterizations is considered. Some new concepts like intuitionistic fuzzy ρ-ideal (IFρi), intuitionistic fuzzy ρ-subalgebra (IFρs), ρ-homomorphism, and intuitionistic fuzzy ρ¯-ideal (IFρ¯i) are introduced and some of their descriptions are given in this work. Further, we show some applications on the family of all intuitionistic fuzzy ρ-subalgebras IFρS(R) in ρ-algebra like the binary relations ≈μ, ≈ν and Γr on IFρS(R). Also, their equivalence classes are given and studied.

We first introduce some new notions of Baireness in fuzzy soft topological space (FSTS). Next, their characterizations and basic properties are investigated in this work. The notions of fuzzy soft dense, fuzzy soft nowhere dense, fuzzy soft meager, fuzzy soft second category, fuzzy soft residual, fuzzy soft Baire, fuzzy soft δ-sets, fuzzy soft λσ-sets, fuzzy soft σ-nowhere dense, fuzzy soft σ-meager, fuzzy soft σ-residual, fuzzy soft σ-Baire, fuzzy soft σ-second category, fuzzy soft σ-residual, fuzzy, fuzzy soft submaximal space, fuzzy soft P-space, fuzzy soft almost resolvable space, fuzzy soft hyperconnected space, fuzzy soft A-embedded, fuzzy soft D-Baire, fuzzy soft almost P-spaces, fuzzy soft Borel, and fuzzy soft σ-algebra are introduced. Furthermore, several examples are shown as well.

In this paper, a color image of encryption algorithm used a graph theory has been proposed. The proposed algorithm depends on the audio files as a basis for exploiting a set of keys for encoding color images. The key generation system was built by passing the audio signal in several stages based on the graph theory. The results revealed that the proposed algorithm has generated the encrypted images with uniform distribution in pixel histograms with information entropy closes to 8, which resists different attacks. The comparison experiments with other recent algorithms were performed. The statistical results show that the proposed algorithm has a strong security against attacks.

In this paper we introduced a new family of L. P. O. ℬ ¯ m ˙ , r ^ which represent a generalization of Bernstein oper. for a continuous function on the interval [0,1] . Our goal is to study the approximation properties of this sequence and study the uniformly convergence of it on some continuous functions on a compact set [0,1]. We find a rate of this convergence using a modulus of continuity. Finally we establish a formula of a Voronoviskaja-type asymptotic formula on ℬ ¯ m ˙ , r ^ .

In this paper, we first introduce and discuss new classes of ideals in − d algebra like M Ideals and S Ideals. Also, we introduce new classes of soft algebras they are called soft S algebras. Next, we use our new connotations to introduce and investigate new concepts in soft S − algebras like soft M − Ideals and soft S − Ideals. In this work, we prove that every S − Ideal is M − Ideal. Moreover, we show that it is not necessary every M − Ideal of ℑ is S − Ideal of ℑ by a counterexample. Also, some properties of our connotations are given.