Heat transfer is a vital fact of daily life, engineering, and industrial mechanisms such as cryogenic systems, spaceborne thermal radiometers, electronic cooling, aircraft engine cooling, aircraft environmental control systems, etc. The addition of nanoparticles helps to stabilize the flowing of a nanofluid and keeps the symmetry of the flowing structure. Purpose: In this attempt, the effect of endothermic/exothermic chemical reactions accompanied by activation energy on a ternary hybrid nanofluid with the geometry of a wedge is taken into consideration. The mathematical form of PDEs is obtained by Navier–Stokes equations, the second law of thermodynamics, and Fick’s second law of diffusion. The geometric model is therefore described using a symmetry technique. Formulation: The MATLAB built-in Lobatto III A structure is utilized to find the computational solution of the dimensionless ODEs. All computational outcomes are presented by graphs and statistical graphs in order to check the performance of various dimensionless quantities against drag force factor and Nusselt quantity. Finding: the addition of tri-hybridizing nanomolecules in the standard liquid improves the thermic performance of the liquid much better in comparison to simple hybrid nanofluids. Wedge angle parameter $\alpha$ brings about a decrement in fluid velocity and augmentation in thermal conductivity $ϵ$, thermal radiation $Rd$, thermophoresis parameter $Nt$ and endothermic/exothermic reaction $\Omega$, and fitted rate constant $n$ accelerates the heat transmission rate. Novelty: The effect of tri-hybridizing nanomolecules along with endothermic/exothermic reactions on the fluid past a wedge have not been investigated before in the available literature.

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.

Irregularity indices are usually used for quantitative characterization of the topological structures of non-regular graphs. In numerous problems and applications, especially in the fields of chemistry and material engineering, it is useful to be aware of the irregularity of a molecular structure. Furthermore, the evaluation of the irregularity of graphs is valuable not only for quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies but also for various physical and chemical properties, including entropy, enthalpy of vaporization, melting and boiling points, resistance, and toxicity. In this paper, we will restrict our attention to the computation and comparison of the irregularity measures of different classes of dendrimers. The four irregularity indices which we are going to investigate are $\sigma$ irregularity index, the irregularity index by Albertson, the variance of vertex degrees, and the total irregularity index.

In recent years, several structure-based properties of the molecular graphs are understood through the chemical graph theory. The molecular graph G of a molecule consists of vertices and edges, where vertices represent the atoms in a molecule and edges represent the chemical bonds between these atoms. A numerical quantity that gives information related to the topology of the molecular graphs is called a topological index. Several topological indices, contributing to chemical graph theory, have been defined and vastly studied. Recent inclusions in the class of the topological indices are the K-Banhatti indices. In this paper, we established the precise formulas for the first and second K-Banhatti, modified K-Banhatti, K-hyper Banhatti, and hyper Revan indices of silicon carbide Si2C3-III[n, m]. In addition, we present the graphical analysis along with the comparison of these indices for Si2C3-III[n, m].

Let I_G be the binomial edge ideal on the generic 2×n - Hankel matrix associated with a closed graph G on the vertex set [n]. We characterize the graphs G for which I_G has maximal regularity and is Gorenstein.

Let $L$ be a distributive lattice and $R[L]$ the associated Hibi ring. We show that if $L$ is planar, then any bounded Hibi subring of $R[L]$ has a quadratic Gr\"obner basis. We characterize all planar distributive lattices $L$ for which any proper rank bounded Hibi subring of $R[L]$ has a linear resolution. Moreover, if $R[L]$ is linearly related for a lattice $L$, we find all the rank bounded Hibi subrings of $R[L]$ which are linearly related too.