A topological index is a map from molecular structure to a real number. It is a graph invariant and also used to describe the physio-chemical properties of the molecular structures of certain compounds. In this paper, we have investigated a chemical structure of pentacene. Our paper reflects the work on the following indices:Rα, Mα, χα, ABC, GA, ABC4, GA5, PM1, PM2, M1(G, p)and M1(G, p) of the para-line graph of linear [n]-pentacene and multiple pentacene.
Topological index sometimes called molecular descriptor is a numerical value which associates a chemical composition for correlating chemical structure with numerous physical properties, chemical reactivity, or biological activity. In this paper, we study some topological indices of boron and try to correlate the physicochemical properties such as freezing points, boiling points, melting points, infrared spectrum, electronic parameters, viscosity, and density of chemical graphs. We discuss these topological indices, and some of them are mentioned here such as Randic index, the first general Zagreb index, the general sum connectivity index, hyper-Zagreb index (HM), the atom-bond connectivity index (ABC), the geometric-arithmetic index (GA), the harmonic index (H), and the forgotten index (F).
Energy of a molecule plays an important role in physics, chemistry and biology. In mathematics, the concept of energy is used in graph theory to help other subjects such as chemistry and physics. In graph theory, nullity is the number of zeros extracted from the characteristic polynomials obtained from the adjacency matrix, and inertia represents the positive and negative eigenvalues of the adjacency matrix. Energy is the sum of the absolute eigenvalues of its adjacency matrix. In this study, the inertia, nullity and signature of the aforementioned structures have been discussed.
A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the AG 2 G and Sanskruti index for the Robertson apex graph G.
Semigroups are generalizations of groups and rings. In the semigroup theory, there are certain kinds of band decompositions which are useful in the study of the structure of semigroups. This research will open up new horizons in the field of mathematics by aiming to use semigroup of h -bi-ideal of semiring with semilattice additive reduct. With the course of this research, it will prove that subsemigroup, the set of all right h -bi-ideals, and set of all left h -bi-ideals are bands for h -regular semiring. Moreover, it will be demonstrated that if semigroup of all h -bi-ideals B H , ∗ is semilattice, then H is h -Clifford. This research will also explore the classification of minimal h -bi-ideal.
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