The symmetry of the graph has always been a hot topic in graph theory and the vertex-transitive graphs are a class of graphs with high symmetry. Cayley graphs which are the highly symmetrical graphs play an important role and much work has been done in the study. The tri-Cayley graph is a natural generalization of the Cayley graph. A graph is said to be a tri-Cayley graph if it admits a semiregular subgroup of automorphisms having three orbits of equal length. Koács et al. classified the cubic symmetric tricirculants in 2012 and Potočnik et al. classified the cubic vertex-transitive tricirculants in 2018. Currently, there is no research on the classification of 4-valent tri-Cayley graphs over cyclic group. In this paper, we will construct two classes of 4-valent tri-Cayley graphs over cyclic group and discuss their automorphism groups. In addition, the vertex transitivity, edge transitivity and arc transitivity are proved.

This paper introduces a rigorous impossibility proof in Euclidean geometry, presenting a scrupulous demonstration of the unattainability of doubling the volume of a cube through any given procedure. The proof methodically follows the rigorous principles of classical geometry, offering clarity and insight into a longstanding mathematical challenge. The paper further emphasizes the historical misconceptions and varied solutions that have emerged due to the lack of a definitive Euclidean geometric proof. It highlights the enduring strengths, independence, and richness of Euclidean geometry while dispelling the notion that algebraic methods are the exclusive avenue to tackle geometric impossibilities. The results obtained throughout this proof solidify the position of Euclidean geometry as a potent and illuminating tool, reaffirming its pivotal role in the world of mathematics. This work contributes not only to the resolution of a specific mathematical challenge but also to the broader understanding of the unique virtues and capabilities of Euclidean geometry in tackling complex geometric problems.

A virus spread by mosquitoes called dengue fever affects millions of people each year and is a serious threat to world health. More than 140 nations are affected by the illness of dengue fever. Therefore, in this paper, a Susceptible-Infectious-Recovered (SIR) mathematical model for the host (human) and vector (dengue mosquitoes) has been presented to describe the transmission of dengue in Bangladesh. In the model the vector are related with two compartments that are susceptible and infective and host are related with three compartments that are susceptible, infective, and recovered. By these five compartments, five connected nonlinear ordinary differential equations (ODEs) are produced. As a result of non dimensionalization, a system of three nonlinear ODEs has been generated. The reproductive number and equilibrium points have been estimated for different cases. In order to compute the infection rate, data for infected human populations have been gathered from multiple health institutes in Bangladesh. MATLAB has been utilized to construct numerical simulations of different compartments in order to examine the impact of critical parameters on the disease’s propagation and to bolster the analytical findings. The simulated outcomes for susceptible, infected, and eliminated in graphical formats have been displayed. The paper’s main goal is to emphasize the uniqueness of computational analysis of the SIR mathematical model for the dengue fever.

At the bedrock of cryptosystems lie trapdoor functions, serving as the fundamental building blocks that determine the security and efficacy of encryption mechanisms. These functions operate as one-way transformations, demonstrating an inherent asymmetry: they are designed to be easily computable in one direction, while proving computationally challenging, if not infeasible, in the opposite direction. This paper contributes to the evolving landscape of cryptographic research by introducing a novel trapdoor function, offering a fresh perspective on the intricate balance between computational efficiency and security in cryptographic protocols.
The primary objective of this paper is to present and scrutinize the proposed trapdoor function, delving into a comprehensive analysis that unveils both its strengths and weaknesses. By subjecting the function to rigorous examination, we aim to shed light on its robustness as well as potential vulnerabilities, contributing valuable insights to the broader cryptographic community. Understanding the intricacies of this new trapdoor function is essential for assessing its viability in practical applications, particularly in securing sensitive information in real-world scenarios.
Moreover, this paper does not shy away from addressing the pragmatic challenges associated with deploying the proposed trapdoor function at scale. A thorough discussion unfolds, highlighting the potential hurdles and limitations when attempting to integrate this function into large-scale environments. Considering the practicality and scalability of cryptographic solutions is pivotal, and our analysis strives to provide a clear understanding of the circumstances under which the proposed trapdoor function may encounter obstacles in widespread implementation.
In essence, this paper contributes to the ongoing discourse surrounding trapdoor functions by introducing a new entrant into the cryptographic arena. By meticulously exploring its attributes, strengths, and limitations, we aim to foster a deeper understanding of the intricate interplay between cryptographic theory and real-world applicability.

Cloud computing has been adopted widely by information systems due to its scalability and availability of resources and services. Cloud computing can provide different types of services through internet for Information Systems (IS). There are many cloud computing providers such as Google, Microsoft, and IBM are seeking for adopting of cloud services. Selecting the suitable cloud provider can maximize the benefits of cloud services. There is a need to determine the suitable cloud computing provider to achieve organizations' goals and maximize the benefits of cloud services. This work aims to introduce a decision support model based on trapezoidal neutrosophic numbers for determining the suitable cloud computing provider. The proposed model is applied by the Zagazig University (ZU) and the results indicated that the model can provide flexible method that can handle uncertainty in decision making for detecting the suitable provider. Also, the results show that the proposed model can support information systems in the choosing the suitable cloud computing provider.