Iranian Journal of Mathematical Chemistry
Volume:14 Issue: 2, Spring 2023

Topological indices are numerical values that correlate a molecular graph’s physical and chemical properties. Titania nanotubes are a well-known semiconductor with a wide range of technological applications including biomedical devices, dye-sensitized solar cells, and so on. We offer two new graph invariants in this study known as the ‘Reformulated Y-index’ and ‘Reformulated S-index’. We calculate some special graphs and the Reformulated Y-index and S-index for some graph operations like as Join, Cartesian Product, Corona product, Corona join product, Subdivision vertex join and evaluate the Titania Nanotubes in Reformulated indices.

In this paper we revisit a nonlinear singular boundary value problem (SBVP) which arises frequently in mathematical model of diffusion and reaction in porous catalysts or biocatalyst pellets. A new simple variant of sinc methods so-called poly-sinc collocation method, is presented to solve non-isothermal reaction-diffusion model equation in a spherical catalyst and reaction-diffusion model equation in an electroactive polymer film. This method reduces each problem into a system of nonlinear algebraic equations, and on solving them by Newton's iteration method, we obtain the approximate solution. Through testing with numerical examples, it is found that our technique has exponentially decaying error property and performs well near singularity like other conventional sinc methods. The obtained results are in good agreement with previously reported results in the literature, and there is an impressive degree of agreement between our results and those obtained by a MAPLE ODE solver. Furthermore, the high accuracy of method is verified by using a residual evaluation strategy.

For an edge e = uv of a graph G, mu(e|G) denotes the number of edges closerto the vertex u than to v (similarly mv(e|G)). The edge Mostar index Moe(G), of a graphG is defined as the sum of absolute differences between mu(e|G) and mv(e|G) over alledges e = uv of G. H. Liu et al. proposed a Conjecture on extremal bicyclic graphs withrespect to the edge Mostar index [1]. Even though the Conjecture was true in case of thelower bound and proved in [2], it was wrong for the upper bound. In this paper, wedisprove the Conjecture proposed by H. Liu et al. [1], propose its correct version andprove it. We also give an alternate proof for the lower bound of the edge Mostar indexfor bicyclic graphs with a given number of vertices.

A rapidly developing field of science and technology is nanobiotechnology. Nanotube, nanostar and polyomino chain are critical and widespread molecular structures extensively used in the domains of pharmaceuticals, chemical engineering, and medical science. Additionally, these structures serve as the foundational building blocks for other, more intricate chemical molecular structures. In this paper, certain chemical structures like nanostar dendrimer, oxide network, silicate network, boron nanosheet and polyomino chains have been acyclically colored using the concept of vertex cut and matching. Also, we determine the acyclic coloring parameters for the networks under consideration and find a relation between them.

The general Randi´c index of a graph G = (V,E) was defined asR_α=∑_(u,v∈V)(d_u d_v )^α , where du is the degree of vertex u and α isan arbitrary real number. In this paper we define the Randi´c indexof a uniform hypergraph and obtain lower and upper bounds for Rαdepending different values of α.