Topological indices have been computed for various molecular structures over many years. These are numerical invariants associated with molecular structures and are helpful in featuring many properties. Among these molecular descriptors, the eccentricity connectivity index has a dynamic role due to its ability of estimating pharmaceutical properties. In this article, eccentric connectivity, total eccentricity connectivity, augmented eccentric connectivity, first Zagreb eccentricity, modified eccentric connectivity, second Zagreb eccentricity, and the edge version of eccentric connectivity indices, are computed for the molecular graph of a PolyEThyleneAmidoAmine (PETAA) dendrimer. Moreover, the explicit representations of the polynomials associated with some of these indices are also computed.

In quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies, computation of topological indices is a vital tool to predict biochemical and physio-chemical properties of chemical structures. Numerous topological indices have been inaugurated to describe different topological features. The ev and ve-degree are recently introduced novelties, having stronger prediction ability. In this article, we derive formulae of the ev-degree and ve-degree based topological indices for chemical structure of Si2C3 − I[a,b].

This article aims to investigate the heat and mass transfer of MHD Oldroyd-B fluid with ramped conditions. The Oldroyd-B fluid is taken as a base fluid (Blood) with a suspension of gold nano-particles, to make the solution of non-Newtonian bio-magnetic nanofluid. The surface medium is taken porous. The well-known equation of Oldroyd-B nano-fluid of integer order derivative has been generalized to a non-integer order derivative. Three different types of definitions of fractional differential operators, like Caputo, Caputo-Fabrizio, Atangana-Baleanu (will be called later as $$C,CF,AB$$C , C F , A B ) are used to develop the resulting fractional nano-fluid model. The solution for temperature, concentration, and velocity profiles is obtained via Laplace transform and for inverse two different numerical algorithms like Zakian’s, Stehfest’s are utilized. The solutions are also shown in tabular form. To see the physical meaning of various parameters like thermal Grashof number, Radiation factor, mass Grashof number, Schmidt number, Prandtl number etc. are explained graphically and theoretically. The velocity and temperature of nanofluid decrease with increasing the value of gold nanoparticles, while increase with increasing the value of both thermal Grashof number and mass Grashof number. The Prandtl number shows opposite behavior for both temperature and velocity field. It will decelerate both the profile. Also, a comparative analysis is also presented between ours and the existing findings.

For a graph , an ordered set is called the resolving set of , if the vector of distances to the vertices in is distinct for every . The minimum cardinality of is termed as the metric dimension of . is called a fault-tolerant resolving set (FTRS) for , if is still the resolving set . The minimum cardinality of such a set is the fault-tolerant metric dimension (FTMD) of . Due to enormous application in science such as mathematics and computer, the notion of the resolving set is being widely studied. In the present article, we focus on determining the FTMD of a generalized wheel graph. Moreover, a formula is developed for FTMD of a wheel and generalized wheels. Recently, some bounds of the FTMD of some of the convex polytopes have been computed, but here we come up with the exact values of the FTMD of two families of convex polytopes denoted as for and for . We prove that these families of convex polytopes have constant FTMD. This brings us to pose a natural open problem about the existence of a polytope having nonconstant FTMD.

This article presents a novel strategy regarding the stabilization control problem for plants with unmatched uncertainties. The methodology is based on Adaptive Smooth Super Twisting Sliding Mode Control. At first, as an initial step, the plant with unmatched uncertainty is transformed into a plant with matched uncertainty. At the second step, the plant with matched uncertainty is decomposed into a unique framework containing the nominal part and some unknown terms (where these unknown terms are computed adaptively). The nominal system is stabilized by using Smooth Super Twisting Sliding Mode Control. The stabilizing controller for the plant with matched uncertainty is designed in a way; it contains some nominal control plus some compensator term. The stability of the said technique is presented impressively. The compensator controller and the adapted laws are derived in such a way that the time derivative of a Lyapunov function becomes strictly negative. The proposed method is tested on a fourth-order plant. The simulation results show the effectiveness and validity of the proposed controller.