Fault-tolerance in metric dimension of boron nanotubes lattices

The concept of resolving set and metric basis has been very successful because of multi-purpose applications both in computer and mathematical sciences. A system in which failure of any single unit, another chain of units not containing the faulty unit can replace the originally used chain is called a fault-tolerant self-stable system. Recent research studies reveal that the problem of finding metric dimension is NP-hard for general graphs and the problem of computing the exact values of fault-tolerant metric dimension seems to be even harder although some bounds can be computed rather easily. In this article, we compute closed formulas for the fault-tolerant metric dimension of lattices of two types of boron nanotubes, namely triangular and alpha boron. These lattices are formed by cutting the tubes vertically. We conclude that both tubes have constant fault tolerance metric dimension 4

Albertson (Alb) spectral radii and Albertson (Alb) energies of graph operation

The sum of the absolute eigenvalues of the adjacency matrix make up graph energy. The greatest absolute eigenvalue of the adjacency matrix is represented by the spectral radius of the graph. Both molecular computing and computer science have uses for graph energies and spectral radii. The Albertson (Alb) energies and spectral radii of generalized splitting and shadow graphs constructed on any regular graph is the main focus of this study. The only thing that may be disputed is the comparison of the (Alb) energies and (Alb) spectral radii of the newly formed graphs to those of the base graph. By concentrating on splitting and shadow graph, we compute new correlations between the Alb energies and spectral radius of the new graph and the prior graph

Hilbert series of mixed braid monoid MB2,2 MB_{2, 2}

Hilbert series is a simplest way to calculate the dimension and the degree of an algebraic variety by an explicit polynomial equation. The mixed braid group $B_{m, n}$ is a subgroup of the Artin braid group $B_{m+n}$. In this paper we find the ambiguity-free presentation and the Hilbert series of canonical words of mixed braid monoid $M\!B_{2, 2}$

ISI spectral radii and ISI energies of graph operations

Graph energy is defined to be the p-norm of adjacency matrix associated to the graph for p = 1 elaborated as the sum of the absolute eigenvalues of adjacency matrix. The graph’s spectral radius represents the adjacency matrix’s largest absolute eigenvalue. Applications for graph energies and spectral radii can be found in both molecular computing and computer science. On similar lines, Inverse Sum Indeg, (ISI) energies, and (ISI) spectral radii can be constructed. This article’s main focus is the ISI energies, and ISI spectral radii of the generalized splitting and shadow graphs constructed on any regular graph. These graphs can be representation of many physical models like networks, molecules and macromolecules, chains or channels. We actually compute the relations about the ISI energies and ISI spectral radii of the newly created graphs to those of the original graph

Antigenic Peptide Prediction From E6 and E7 Oncoproteins of HPV Types 16 and 18 for Therapeutic Vaccine Design Using Immunoinformatics and MD Simulation Analysis

Human papillomavirus (HPV) induced cervical cancer is the second most common cause of death, after breast cancer, in females. Three prophylactic vaccines by Merck Sharp & Dohme (MSD) and GlaxoSmithKline (GSK) have been confirmed to prevent high-risk HPV strains but these vaccines have been shown to be effective only in girls who have not been exposed to HPV previously. The constitutively expressed HPV oncoproteins E6 and E7 are usually used as target antigens for HPV therapeutic vaccines. These early (E) proteins are involved, for example, in maintaining the malignant phenotype of the cells. In this study, we predicted antigenic peptides of HPV types 16 and 18, encoded by E6 and E7 genes, using an immunoinformatics approach. To further evaluate the immunogenic potential of the predicted peptides, we studied their ability to bind to class I major histocompatibility complex (MHC-I) molecules in a computational docking study that was supported by molecular dynamics (MD) simulations and estimation of the free energies of binding of the peptides at the MHC-I binding cleft. Some of the predicted peptides exhibited comparable binding free energies and/or pattern of binding to experimentally verified MHC-I-binding epitopes that we used as references in MD simulations. Such peptides with good predicted affinity may serve as candidate epitopes for the development of therapeutic HPV peptide vaccines

M-Polynomials and Topological Indices of Titania Nanotubes

Titania is one of the most comprehensively studied nanostructures due to their widespread applications in the production of catalytic, gas sensing, and corrosion-resistant materials. M-polynomial of nanotubes has been vastly investigated, as it produces many degree-based topological indices, which are numerical parameters capturing structural and chemical properties. These indices are used in the development of quantitative structure-activity relationships (QSARs) in which the biological activity and other properties of molecules, such as boiling point, stability, strain energy, etc., are correlated with their structure. In this report, we provide M-polynomials of single-walled titania (SW TiO2) nanotubes and recover important topological degree-based indices to theoretically judge these nanotubes. We also plot surfaces associated to single-walled titania (SW TiO2) nanotubes

Some Invariants of Jahangir Graphs

In this report, we compute closed forms of M-polynomial, first and second Zagreb polynomials and forgotten polynomial for Jahangir graphs Jn,m for all values of m and n. From the M-polynomial, we recover many degree-based topological indices such as first and second Zagreb indices, modified Zagreb index, Symmetric division index, etc. We also compute harmonic index, first and second multiple Zagreb indices and forgotten index of Jahangir graphs. Our results are extensions of many existing results

Presentation1_Exploring spectrum-based descriptors in pharmacological traits through quantitative structure property (QSPR) analysis.pdf

The study centered on Quantitative Structure Property Relationship (QSPR) analysis with a focus on various graph energies, investigating drugs like Mefloquinone, Sertraline, Niclosamide, Tizoxanide, PHA-690509, Ribavirin, Emricasan, and Sofosbuvir. Employing computational modeling techniques, the research aimed to uncover the correlations between the chemical structures of these medications and their unique properties. The results illuminated the quantitative relationships between structural characteristics and pharmacological traits, advancing our predictive capabilities. This research significantly contributes to medication discovery and design by providing essential insights into the structure-property connections of these medicinal compounds. Notably, certain spectrum-based descriptors, such as positive inertia energy, adjacency energy, arithmetic-geometric energy, first zegrab energy, and the harmonic index, exhibited strong correlation coefficients above 0.999. In contrast, well-known descriptors like the Extended adjacency, Laplacian and signless Laplacian spectral radii, and the first and second Zagreb Estrada indices showed weaker performance. The article emphasizes the application of graph energies and a linear regression model to predict pharmacological features effectively, enhancing the drug discovery process and aiding in targeted drug design by elucidating the relationship between molecular structure and pharmacological characteristics.</p

On the Metric Dimension of Generalized Tensor Product of Interval with Paths and Cycles

The concept of minimum resolving set for a connected graph has played a vital role in Robotic navigation, networking, and in computer sciences. In this article, we investigate the values of m and n for which P2⊗mPn and P2⊗mCn are connected and find metric dimension in this case. We also conclude that, for each m, we obtain a new regular family of constant metric dimension. We also give a basis for these graphs and presentation of resolving vector in general closed form with respect to the basis