In this study, we delve into the evaluation of graph entropy through the lens of topological properties inherent in crystallographic structures. Specifically, we focus on the crystallographic structure of TiF2[i,j,t] (Figure 1). By employing various topological indices to compute the entropies of TiF2[i,j,t]. This comprehensive approach allows for a deeper understanding of the entropy characteristics of this particular crystallographic structure, offering insights into its inherent properties.

These days, the best way to secure our data and conversations is to use message encryption techniques. Thanks to the proliferation of network and internet communications, advancements in message encryption technologies have picked up speed. When personal, sensitive information is transmitted via unsecured networks, it opens the door to possible hacking attempts, theft, and eavesdropping on conversations. In order to shorten this term, cryptographic methods are essential. Along with the conventional matrix algebra, we created a higher-order recursive matrix called an Extended generalised Lucas matrix and linked it to Extended generalised Fibonacci sequences in this paper. Elliptic curve cryptography and graph theory are the foundations of our proposed public key cryptography, which employs these matrices as keys for an affine cypher and key agreement for encryption-decryption using a mix of terms from Extended generalised Lucas sequences and residue operations. By reducing key transmission to the exchange of a small set of numbers (parameters) rather than the full key matrix, this method offers a large key space while simultaneously reducing the space and time complexity of key transmission. On top of that, it’s secure and dependable since it’s built on the challenging Elliptic Curve-Discrete Logarithm algorithm.

Graph theory as part of mathematics, has experienced significant development from the theoretical aspect, one of it is the theory of metric dimension. The concept of metric dimensions has evolved greatly, including the dominant metric dimension and the complement metric dimension. In this study, the concept of the central metric dimension is introduced, that is a combination of the metric dimension and central of a graph. The minimum number of vertices of a resolver set that contains a central set is called the central metric dimension of graph G, and denoted by dimcen(G). Several characterizations of a graph having a certain central metric dimension are yielded in this study. Several relations are obtained between the central metric dimension and the metric dimension. Furthermore, the central metric dimension is applied on edge coronation graphs. The edge coronation of graphs G and H is denoted by (G ◊ H). The results of the study show that the central metric dimension of edge coronation of G and H are influenced by the central set and the order of graph G and the metric dimension of graph H.

In today’s world of Ubiquitous Computing, Network security plays an important role in preventing and reducing the chances of various network attacks and working on the various cryptographic algorithms to reduce the risk of getting affected. It is also a challenging situation to reduce the energy consumption of nodes and increasing the life time of sensor nodes. In this paper, Threshold Cryptography is studied and a novel cryptographic algorithm using multi node cryptography for text and image data is proposed. The proposed algorithm is an asymmetric cryptographic algorithm, which uses a key of variable length and encrypts the text and image files (all formats) and provides 2 factor encryption tothe data. The proposed algorithm is fast, lightweight, simple and offers a 2 factor protection to the data which makes it suitable for low resource devices.

A uniserial module is a module that satisfies both ascending chain condition and descending chain condition, which makes a uniserial module an Artinian module and a Noetherian module at the same time. Recently an algebraic structure from ring theory, called almost prime ideal, is generalized into a module theory and called an almost prime submodule. Some researchers have examined the characterizations of this new algebraic structure in various types of modules. In this article, we provide some insights into the almost prime submodule of a uniserial cyclic module In this study, we have discovered that the non-zero almost prime submodule of the cyclic uniserial module is unique.

We provide a simple proof for a complementary pair of group codes over a finite noncommutative Frobenius ring of the fact that one of them is equivalent to the other one. We also explore this fact for checkeable codes over the same type of alphabet.

The concepts of intuitionistic fuzzy BZ – ideal (IFBZ – I) in BZ – algebra (BZ – A) and intuitionistic fuzzy BZ – subalgebra (IFBZ – SA) will be presented and analyzed in this work. Furthermore, the operations on (IFBZ – SA) will be examined. In this study, we demonstrate that for any t ∈ [0,1], if the t – cut of intuitionistic fuzzy π is a (BZ – A), then π is (IFBZ – SA) of X. Also, if π is (IFBZ – SA) of X, then t-cut of intuitionistic fuzzy π is a (BZ – A) of X, for any t ∈ [0,1]. Also, some results about the concepts of this work are shown.

Various methods are utilized providing complexity for cryptosystem with the aim to increase the security and avoiding hacker attack. Hybrid cryptosystem is one of these cryptosystems which is used two types of cryptosystems and has many applications in data transmitted. This research, proposed a novel method that used power exponent instead of using the prime number directly and also providing complexity of asymmetric cryptosystems. This method has been applied theoretically in two public systems RSA and EL-Gamal. Power RSA and Power EL-Gamal are modified asymmetric cryptosystems, in which the power number is kept by the sender and the receiver. Moreover, we use group theory to prove that these cryptosystems work properly. Our extensive studies indicated that our proposed encrypt and decrypt method provides increased security against hackers.

The present article is to study a certain cases for resolutions two rows for Weyl module, where F & DrƑ are free modules over a commutative ring R & divided power algebra for degree r, respectively in the cases for the skew-partition (9,6)/(2,0) & (9,6)/(3,0). Two cases for resolution. Weyl modules are associated with the two-row skew-partition when the second row comes forward to the left for the first, creeping two & three in different cases. To determine the limits for that characteristic-free element & f& the exactness for the Weyl resolution, simply describe contracting homotopy for the skew-partition using a homological approach, which means the letter-place techniques, contracting homotopy, “place polarization”.

This work introduces the Kuffi- Abbas- Jawad transform, also known as the KAJintegral transformation. We discuss key KAJ- transition properties and their cryptographic applications. An application is presented to demonstrate how to encrypt a plaintext and decrypt it using the KAJ- transform technique and inverse KAJ- transform, respectively.