Ordering Unicyclic Connected Graphs with Girth g ≥ 3 Having Greatest SK Indices

For a graph, the SK index is equal to the half of the sum of the degrees of the vertices, the SK1 index is equal to the half of the product of the degrees of the vertices, and the SK2 index is equal to the half of the square of the sum of the degrees of the vertices. This paper shows a simple and unified approach to the greatest SK indices for unicyclic graphs by using some transformations and characterizes these graphs with the first, second, and third SK indices having order r ≥ 5 and girth g ≥ 3, where girth is the length of the shortest cycle in a graph.

M-Polynomials and Degree-Based Topological Indices of the Molecule Copper(I) Oxide

Topological indices are numerical parameters used to study the physical and chemical residences of compounds. Degree-based topological indices have been studied extensively and can be correlated with many properties of the understudy compounds. In the factors of degree-based topological indices, M-polynomial played an important role. In this paper, we derived closed formulas for some well-known degree-based topological indices like first and second Zagreb indices, the modified Zagreb index, the symmetric division index, the harmonic index, the Randić index and inverse Randić index, and the augmented Zagreb index using calculus.

Computing Zagreb and Randić Indices of PEG-Cored Dendrimers Used for Drug and Gene Delivery

Zagreb and Randić indices are the most commonly used degree-based topological indices in the study of drug design and development. In molecular topology, M-polynomials are also used to calculate the degree-based topological indices of chemical structures. In this paper, we derive the M-polynomials for the PEG-cored PAMAM, carbosilane, and poly (lysine) dendrimers and calculate their first, second, and second modified Zagreb indices and the Randić index.

Some topological indices of dendrimers determined by their Banhatti polynomials

Several properties of chemical compounds in a molecular structure can be determined with the aid of mathematical languages provided by various types of topological indices. In this paper, we consider eight dendrimer structures in the context of valency based topological indices. We define four Banhatti polynomials for general (molecular) graphs, and compute them for underline dendrimers. We use these polynomials to determine four Banhatti indices. We also determine Zagreb (first, second and hyper) and forgotten indices by developing their relationships with Banhatti indices.

Zagreb Polynomials and redefined Zagreb indices of Dendrimers and Polyomino Chains

Dendrimers have an incredibly strong potential because their structure allows multivalent frameworks, i.e. one dendrimer molecule has many possible destinations to couple to a functioning species. Researchers expected to utilize the hydrophobic conditions of the dendritic media to lead photochemical responses that make the things that are artificially tested. Carboxylic acid and phenol- terminated water-dissolvable dendrimers were joined to set up their utility in tranquilize conveyance and furthermore driving compound reactions in their inner parts. This may empower scientists to associate both concentrating on atoms and medication particles to the equivalent dendrimer, which could diminish negative manifestations of prescriptions on sound and health cells. Topological indices are numerical numbers associated with the graphs of dendrimers and are invariant up to graph isomorphism. These numbers compare certain physicochemical properties like boiling point, strain energy, stability, etc. of a synthetic compound. There are three main types of topological indices, i.e degree-based, distance-based and spectrum-based. In this paper, our aim is to compute some degree-based indices and polynomials for some dendrimers and polyomino chains. We computed redefined first, second and third Zagreb indices of PAMAM dendrimers PD1, PD2, and DS1 and linear Polyomino chain Ln , Zigzag Polyomino chain Zn, polyomino chain with n squares and of m segments $B_{n}^{1}$and $B_{n}^{2}$We also computed some Zagreb polynomials of understudy dendrimers and chains.

Irregularity of Block Shift Networks and Hierarchical Hypercube Networks

There is extremely a great deal of mathematics associated with electrical and electronic engineering. It relies upon what zone of electrical and electronic engineering; for instance, there is much increasingly theoretical mathematics in communication theory, signal processing and networking, and so forth. Systems include hubs speaking with one another. A great deal of PCs connected together structure a system. Mobile phone clients structure a network. Networking includes the investigation of the most ideal method for executing a system. Graph theory has discovered a significant use in this zone of research. In this paper, we stretch out this examination to interconnection systems. Hierarchical interconnection systems (HINs) give a system to planning systems with diminished connection cost by exploiting the area of correspondence that exists in parallel applications. HINs utilize numerous levels. Lower-level systems give nearby correspondence, while more significant level systems encourage remote correspondence. HINs provide issue resilience within the sight of some defective nodes and additionally interfaces. Existing HINs can be comprehensively characterized into two classes: those that use nodes or potential interface replication and those that utilize reserve interface nodes.

Irregularity Indices of Dendrimer Structures Used as Molecular Disrupter in QSAR Study

Dendrimers are rising polymeric structures known for their flexibility in medication conveyance and high usefulness, whose properties are same biomolecules. These nanostructured macromolecules have shown potential capacities in capturing as well as conjugating the high subatomic weight hydrophilic/hydrophobic substances by host-visitor collaborations and covalent holding (prodrug approach) individually. In quantitative structure-property relationships (QSPR), topological indices are utilized to gather properties of dendrimers. Topological indices catch symmetry of dendrimer structures and give it a logical reasoning to predict properties, for instance, viscosity, boiling points, the radius of gyrations, etc. In this report, we intend to examine dendrimers through irregularity indices that are valuable in QSPR studies. We studied sixteen irregularity indices if diverse dendrimer structures.

Computations of the M-Polynomials and Degree-Based Topological Indices for Dendrimers and Polyomino Chains

Topological indices correlate certain physicochemical properties like boiling point, stability, and strain energy of chemical compounds. In this report, we compute M-polynomials for PAMAM dendrimers and polyomino chains. Moreover, by applying calculus, we compute nine important topological indices of under-study dendrimers and chains.

Some Reverse Degree-Based Topological Indices and Polynomials of Dendrimers

Topological indices collect information from the graph of molecule and help to predict properties of the underlying molecule. Zagreb indices are among the most studied topological indices due to their applications in chemistry. In this paper, we compute first and second reverse Zagreb indices, reverse hyper-Zagreb indices and their polynomials of Prophyrin, Propyl ether imine, Zinc Porphyrin and Poly (ethylene amido amine) dendrimers.