Calculation

On the Trinajstic index of zero divisor graphs

2024-12-24T10:15:50+00:00

In this paper, the Trinajstic index, a novel topological index, is analyzed within the framework of basic concepts in Graph Theory, particularly focusing on Zero-Divisor Graphs, excluding trees. The Trinajstic index, initially developed in the context of Chemical Graph Theory, investigates chemical structures based on a distance-balance concept. After constructing a pseudocode to calculate the Trinajstic index, the relevant algorithms were implemented using MATLAB. Subsequently, MATLAB codes for generating graphs and calculating the Trinajstic index were combined to compute the index for various graphs. Formulas relating to prime-based Zero-Divisor Graphs were derived and proven.

A note on Pointwise hemi-slant conformal submersions

2025-03-06T07:18:36+00:00

The current study investigates the concept of pointwise hemi-slant conformal submersions from almost contact metric manifolds to Riemannian manifold. We investigate the geometrical implications of the horizontal and vertical vector fields $\xi$ while studying the distribution integrability and total geodesicness of distribution leaves. Finally, we explore $\phi$-pluriharmonicity from the almost contact metric manifold.

Geometric study of Ricci solitons in perfect fluid spacetimes with Lorentzian concircular structure manifolds

2025-05-06T09:20:37+00:00

In this article, we examine the interaction between Ricci solitons and the properties of the geometric structure in a perfect fluid spacetimes that admits a Lorentzian Concircular structure manifold with a Concircular curvature tensor. We investigate the conditions under which a Ricci soliton exists within such a framework and analyze its implications on the curvature properties of the spacetime. The study focuses on the influence of the soliton potential on the energy-momentum tensor of the perfect fluid and examines the interplay between the Ricci curvature and the Concircular structure. Further, we establish key geometric conditions that characterize the nature of the Ricci soliton in this setting and derive significant constraints on the manifolds topology. Our findings contribute to the broader understanding of the role of Ricci solitons in relativistic fluids and their impact on spacetime geometry.

Tauberian theorems in neutrosophic n-normed linear spaces via statistical Cesaro summability

2025-05-07T18:15:56+00:00

In this study, the connection between statistical Cesaro summability as well as sequence of statistical convergence within neutrosophic n-normed linear space $\mathfrak{(NnNLS)}$ is investigated. Although Cesaro summability along with its statistical variant within classical normed spaces, fuzzy, intuitionistic fuzzy, and neutrosophic are covered in the literature, this study is notable for both its methodology and its thorough approach, which covers a wider range among spaces in addition explains the process beginning with the statistical Cesaro summability concepts towards statistical convergence. The Tauberian theorems in $\mathfrak{NnNLS}$ will follow from these findings.

The integrability for the derivative formulas of the type-2 2 Bishop frame and its applications

2025-06-19T13:33:02+00:00

The main objective of the work is to examine the integrability of the derivative formulae for the type-2 Bishop frame in three-dimensional Euclidean space. We use the coordinate system introduced in \cite{yer1}, which allows for the examination of integration. As an application, we analyze the position vectors of certain curves that are important in mathematics and physical study.