Selvaraj Balachandran

Topological indices can be used to characterize molecular topology. These are numerical measurements of a suggested molecule’s fundamental structural characteristics, derived from its molecular structure. This numerical value, which is derived from a chemical configuration, represents the important physical properties of the proposed molecule. We use an algebraic number to connect the chemical composition with various physical characteristics, biological activity, and chemical reactivity. A graph with a vertex set of [Formula: see text] in which two unique vertices are adjacent when one element is an integral power of the other is called a power graph [Formula: see text] of a finite group [Formula: see text]. This paper investigates several types of topological indices of power graphs for different finite groups based on distance, degree, and independent sets. We compute the Hyper Wiener Index, Degree Distance Index, Additively Weighted Harary Index, Gutman Index, Multiplicatively Weighted Harary Index, Eccentric Connectivity Index, Connective Eccentricity Index, and Merrifield–Simmons Index of power graphs for finite cyclic and non-cyclic groups of order [Formula: see text], dihedral and generalized quaternion groups, where [Formula: see text] are distinct primes. As a consequence, we fix the flaws in the results of Ali et al. [Power graphs of finite groups determined by Hosoya properties, Entropy 24(2) (2022) 213] and present their correct forms.

In today's digital world, recommendation systems are like smart tools that make our online experiences better. Personalized recommendation systems have become a powerful tool for people who would rather improve and control their own health in the ever-changing healthcare environment of today. Even in situations when an individual is on their own, these systems leverage the power of digital technology and data analysis to provide personalized guidance and support for a range of healthcare tasks. Personalized recommendation systems provide customized solutions that consider the unique requirements and preferences of single people, whether the issue is managing mental health concerns, adhering to a balanced diet, managing chronic illnesses, or sustaining physical activity. By using these systems to their full potential, people may take charge of their health and well-being, making educated decisions and achieving their healthcare goals with more confidence and efficiency.

The chapter highlights a novel approach towards predicting blood pressure without the necessity of using invasive methods like cuff-based measurements. This chapter proposes the use of vibration sensors based on the Doppler principle to capture movements within the blood vessels, primarily the movement of arterial walls. The signals acquired from vibration sensor technology are analysed with the various characteristics of cardiovascular dynamics and deployed advanced Spectro-temporal deep learning approaches, thereby predicting blood pressure in real-time and with great precision. In recent years, there has been a sudden proliferation of cuffless blood pressure devices, faring away from the standard method of inflating a cuff around the limb. These devices could hold immeasurable promise in providing continuous, beat-to-beat blood pressure monitoring, creating a more informative record of cardiovascular health trends. Beyond traditional clinical settings, there is application potential for telemedicine, wearables, and integrated healthcare systems.

In this study, we aim to determine the unique tetracyclic graph that maximizes the signless Laplacian Estrada index (SLEE) among all tetracyclic graphs. The SLEE of a graph ? is defined as the sum of the exponentials of its eigenvalues, expressed as follows: SLEE(?)=?n,i=1 esi, where s1, s2,...,sn are the eigenvalues of the signless Laplacian matrix of ?. By identifying this unique tetracyclic graph, we desire to understand the specific structural characteristics that contribute to the maximum SLEE within the class of tetracyclic graphs.

Let [ ] be a simple connected graph. The first Zagreb index denoted by [ ] is defined as [ ]. We present a lower bound for [ ] in terms of order and edge-vertex domination number for trees and characterized the extremal trees attaining the bound.

Let [ ] be a simple connected graph. The modified first Zagreb index is denoted by [ ] is defined as [ ]. We present a lower bound for [ ] in terms of order and total domination number for trees and characterize the extremal trees attaining the bound.

Topological indices are numerical graph invariants generated from molecular graphs of chemicals to explain their structural properties. The atom-bond sum-connectivity (ABS) index and Randić (R) index are among the widespread graph invariants. The central theme of this work is the difference between these two indices, which is formulated for a graph G as ABS(G)-R(G)=\sum\limits_{fg\in E(G)} \dfrac{1}{\sqrt{d_fd_g(d_f+d_g)}} \left(\sqrt{d_fd_g(d_f+d_g-2)}-\sqrt{d_f+d_g}\right), where d_f stands for the degree of the vertex f in graph G. The primary objective of the article is to identify extremals over the set of all binary trees and chemical trees for ABS(G)-R(G). Furthermore, we aim to examine the significance of ABS(G)-R(G) in the structure-property modelling of molecules.