Weighted Mostar indices as measures of molecular peripheral shapes with applications to graphene, graphyne and graphdiyne nanoribbons

On degree-based operators and topological descriptors of molecular graphs and their applications to QSPR analysis of carbon derivatives

This work initiates a concept of reduced reverse degree basedRR D M -Polynomial for a graph, and differential and integral operators by using thisRR D M -Polynomial. In this study twelve reduced reverse degree-based topological descriptors are formulated using theRR D M -Polynomial. The topological descriptors, denoted as T D 's, are numerical invariants that offer significant insights into the molecular topology of a molecular graph. These descriptors are essential for conducting QSPR investigations and accurately estimating physicochemical attributes. The structural and algebraic characteristics of the graphene and graphdiyne are studied to apply this methodology. The study involves the analysis and estimation of Reduced reverse degree-based topological descriptors and physicochemical features of graphene derivatives using best-fit quadratic regression models. This work opens up new directions for scientists and researchers to pursue, taking them into new fields of study.

On Certain Degree Based and Bond-additive Topological Indices of Dodeca-benzo-circumcorenene

BACKGROUND

Chemical graph theory has been used to mathematically model the various physical and biological aspects of chemical substances. A mathematical formulation that may be applied to any graph and can characterise a molecule structure is known as a topological index or molecular descriptor.

METHOD

It is convenient and efficient to analyse the mathematical values and further research on various physical properties of a molecule based on these molecular descriptors. They provide useful alternatives to lengthy, expensive, and labour-intensive laboratory experiments. The topological indices can be used to predict the chemical structures, physicochemical properties, and biological activities using quantitative structure-activity relationships (QSARs) and quantitative structure-property relationships (QSPRs).

RESULT

In this study, the molecular descriptors of the Dodeca-benzo-circumcorenene compounds are derived based on their corresponding molecular structures.

CONCLUSION

The computed indices are then compared graphically to study their relationship with the molecular structure and with each other..

Computation of Polynomial Degree-Based Topological Descriptors of Indu-Bala Product of Two Paths

Cheminformatics is entirely a newly coined term that encompasses a field that includes engineering computer sciences along with basic sciences. As we all know, vertices and edges form a network whereas vertex and its degrees contribute to joining edges. The degree of vertex is very much dependent on a reasonable proportion of network properties. There is no doubt that a network has to have a reliance of different kinds of hub buses, serials, and other connecting points to constitute a system that is the backbone of cheminformatics. The Indu-Bala product of two graphs $G_1$ and $G_2$ has a special notation as described in Section 2. The attainment of this product is very much due to related vertices at to different places of $G_1\vee G_2$ . This study states we have found M-polynomial and degree-based topological indices for Indu-Bala product of two paths $P_k$ and $P_j$ for $j,k\ge 2$ . We also give some graphical representation of these indices and analyzed them graphically.

Edge Mostar Indices of Cacti Graph With Fixed Cycles

Topological invariants are the significant invariants that are used to study the physicochemical and thermodynamic characteristics of chemical compounds. Recently, a new bond additive invariant named the Mostar invariant has been introduced. For any connected graph ℋ , the edge Mostar invariant is described as M o e ( ℋ ) = ∑ g x ∈ E ( ℋ ) | m ℋ ( g ) - m ℋ ( x ) | , where m ℋ ( g ) ( or  m ℋ ( x ) ) is the number of edges of ℋ lying closer to vertex g (or x) than to vertex x (or g). A graph having at most one common vertex between any two cycles is called a cactus graph. In this study, we compute the greatest edge Mostar invariant for cacti graphs with a fixed number of cycles and n vertices. Moreover, we calculate the sharp upper bound of the edge Mostar invariant for cacti graphs in ℭ ( n , s ) , where s is the number of cycles.