Topological indices are numerical descriptors that aid in the prediction of chemical molecules’ physiochemical properties and biological actions. It is often helpful to forecast numerous physiochemical attributes and biological actions of molecules in chemometrics, bioinformatics, and biomedicine. In this paper, we establish the M-polynomial and NM-polynomial of some very familiar biopolymers, which are xanthan gum, gellan gum, and polyacrylamide. The uses of these biopolymers can increasingly take the place of traditional admixtures for the application of soil stability and enhancement. We recover the important topological degree-based indices. Also, we give diverse graphs of topological indices and their relations with the parameters of structures.
The most abundant polycarbonates that are found in food are polysaccharides. A long chain of monosaccharide with glycosidic linkages forms polymeric carbohydrates. These carbohydrates with water in the process of hydrolysis produces sugar monosaccharides or oligosaccharides. The examples of polysaccharides include starch, galactogen, and glycogen. They contribute various applications mainly in food storage, pharmaceutical industry, and petroleum extraction. In this work, a polysaccharide known as guar gum is studied and also ten degree-based topological indices, namely, Zagreb indices, Randic index, general Randic index, forgotten index, ABC index, GA index, GH index, Sombor index, and SS index are computed. The chemical derivatives of guar gum such as HPG, CMG, and CMHPG are studied, and topological indices are determined. Finally, numerical and graphical comparison of all the above said ten indices are made for guar gum and its chemical derivatives.
Binary and [Formula: see text]-ary trees have extensive applications, particularly in computer science and chemistry. We present exact values of all important distance-based indices for complete [Formula: see text]-ary trees. We solve recurrence relations to obtain the value of the most well-known index called the Wiener index. New methods are used to express the other indices (the degree distance, the eccentric distance sum, the Gutman index, the edge-Wiener index, the hyper-Wiener index and the edge-hyper-Wiener index) as well. Values of distance-based indices for complete binary trees are corollaries of the main results.
Glycogen is a polysaccharide that has a large number of highly branched polymers. It has a structure that is nearly identical to that of amylopectin. It can be found in practically all animal cells and some plant cells. Glycogen is a natural polysaccharide polymer with features that make it a good antiparticle carrier for cancer therapeutics. It is not only biocompatible by nature but also be chemically modified to accommodate additional molecular components. Topological indices are used to create quantitative structure-activity relationships (QSARs), in which the biological activity or other properties of molecules are linked to their chemical structure. We estimated certain K ^ Banhatti and Gourava indices of natural polymers of polysaccharides, namely, glycogen and amylopectin, which have therapeutic applications, extraordinary features, and fascinating molecular framework, in this study. We also discovered some relationships between K ^ Banhatti indices and information entropies, as well as a relationship between Gourava indices and their respective information entropies. In addition, we give a comparative analysis of these macromolecule families using graphs to highlight their nature.
Porous material such as metal-natural constructions and their particular partner metal-natural poly-hydra are made up of inorganic clusters with no saturation and exhibit great capability for utilization in the absorption of gas and ascending opening in optics and detecting biotechnology and hardware. Cuboctahedral bi-metallic structure is an often-quoted example of metal-natural polyhedra class. In this study, we have calculated the first and second Zagreb index, the augmented Zagreb index, and the inverse Randic, as well as general Randic index, the symmetric division, and harmonic index. We have also discussed these topological indices graphically and have found that the value of almost all indices goes higher and higher as the value of n goes higher.
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