On the Basis of Invariants of Labeled Molecular Graphs

A chemical graph is a mathematical representation of a chemical compound in which atoms and bonds are represented by nodes and lines respectively. Chemists have developed a number of useful tools from graph theory, such as topological index (TI) is structural descriptor or connectivity index used to express molecular size, branching, heat of formation, boiling points, strain energy, toughness and acyclicity. The Topological index is beneficial to establish an association between arrangement and chemical properties of chemical compounds without performing any testing. It is characterized into various categories like degree, distance, spectrum and eccentricity based. This paper consists of computation of multiplicative degree based topological indices namely multiplicative Zagreb indices, multiplicative atom bond connectivity index and generalized multiplicative geometric arithmetic index for SiC_3-I[j, k] and SiC_3-II[j, k].

Journal of Mathematical Chemistry, 1988

Whereas tile internal fragment topological index (IFTI) is calculated in the normal manner as for any molecule, the external fragment topological index (EFTI) is calculated so as to reflect the interaction between the excised fragment Fand the remainder of tile molecule (G-F). For selected topological indices (TIs), a survey of EFTI values, formulas and examples is presented. Some requirements as to the fragment indices arc formulated and examined. In the discussion of the results, it is sho~n that for some Tis regularities exist in the dependence of EFTI values upon the branching of fragment F, or upon the marginal versus central position of the fragment F in the graph G. New vertex invariants can be computed as EFTI values for one-atom fragments over all graph vertices; by iteration, it is in principle possible to devise an infinite number of new vertex invariants.

If G = (V E) is a molecular graph, and d u is the degree of its vertex u , then the first and second Zagreb indices are u∈V d 2 u and uv∈E d u d v , respectively. These molecular structure descriptors, introduced in the 1970s, have been much studied. Yet, a number of their properties, that seem to have evaded attention so far, are established in this work for the first time. Also a more recent degree-based descriptor, the geometric-arithmetic index, equal to

Journal of Chemical Education, 1992

Symmetry

A Topological index also known as connectivity index is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are numerical parameters of a graph which characterize its topology and are usually graph invariant. In QSAR/QSPR study, physico-chemical properties and topological indices such as Randi c ´ , atom-bond connectivity (ABC) and geometric-arithmetic (GA) index are used to predict the bioactivity of chemical compounds. Graph theory has found a considerable use in this area of research. In this paper, we study HDCN1(m,n) and HDCN2(m,n) of dimension m , n and derive analytical closed results of general Randi c ´ index R α ( G ) for different values of α . We also compute the general first Zagreb, ABC, GA, A B C 4 and G A 5 indices for these Hex derived cage networks for the first time and give closed formulas of these degree-based indices.

Journal of Structural Chemistry, 1990

Scientific Reports, 2023

Counting Polynomial is the mathematical function that was initially introduced for application in chemistry in 1936 by G. Polya. Partitioning of graphs can be seen in the coefficients of these mathematical functions, which also reveal the frequency with which these partitions happen. We developed a novel and efficient method for constructing the necessary counting polynomials for a zigzag-edge coronoid formed by the fusion of a Starphene graph and a Kekulenes graph. The study's methods expand our knowledge, and its findings potentially provide insight on the topology of these chemical structures. .Graph theory has several applications beyond the chemistry, including the study of chemical compounds, which are often represented as graphs. The chemical compound's graph can be represented by a molecular descriptor, a matrix, or a graph polynomial. Using the applications of Chemical Graph Theory, we reveal that the graph polynomials, molecular descriptors, and sequences associated to molecular descriptors for 2D-molecular graphs have significant implications for the domains of mathematical chemistry, quantum chemistry, QSAR, and QSPR. Moreover the Chemical graph theory or Molecular topology is a branch of Graph theory applied in the study of molecular structures represents an interdisciplinary science. Topological characterization of chemical structures allows the classification and modelling of structures with desired properties. The counting polynomials show the partition of graphical structures such as, the Omega and Theta polynomials, which count the equidistance edges, whereas Sadhana and PI polynomials count the non-equidistance edges that are discussed in the point raised in the first question. Mathematical chemistry is a field of study concerned with innovative applications of mathematics to chemistry. It is primarily concerned with the mathematical modelling of chemical reactions. Mathematical chemistry is also known as computer chemistry; however, it is not to be confused with computational chemistry. Chemical graph theory, which deals with topology such as the mathematical study of isomerism and the development of topological descriptors or indices that find application in quantitative structure-property relationships; and chemical aspects of group theory, which finds applications in stereochemistry and quantum chemistry, are major areas of research in mathematical chemistry. In mathematical chemistry the division of the graph (chemical compound) is shown by counting polynomials, and molecular descriptors are generated using these polynomials. The varied features of the chemical compound are shown by mathematical modelling of the molecular descriptors. We can grasp the structural properties of a chemical compound because it comprises graph polynomials such as counting polynomials, matching polynomials, and differential polynomials. Topological indices related to counting polynomials have been extensively investigated in mathematical chemistry via techniques of graph theory, and they have numerous applications in chemistry, especially in quantum chemistry. Please refer to for any more information that you may require. In recent years, numerous researchers have focused on formula construction and counting polynomials to construct molecular descriptions of various families of molecular graphs. In the field of chemical graph theory, Diudea's research concentrated on counting polynomials and the associated indices for a variety of distinct chemical structures, and he made significant contributions to chemical

Journal of Chemical Information and Modeling, 1996

A highly discriminating molecular topological index, EAID, is proposed based on the extended adjacency matrix. A systematic search for degeneracy was performed for 3 807 434 alkane trees, 202 558 complex cyclic or polycyclic graphs, and 430 472 structures containing heteroatoms. No counterexamples (two or more nonisomorphic structures with the same EAID number) were found. This is a hitherto unheard of power of discrimination. Thus EAID might be possibly used as supplementary reference for CAS Registry Numbers for structure documentation.

Discrete & Continuous Dynamical Systems - S

Topological indices defined on molecular structures can help researchers better understand the physical features, chemical reactivity, and biological activity. Thus, the study of the topological indices on chemical structure of chemical materials and drugs can make up for lack of chemical experiments and can provide a theoretical basis for the manufacturing of drugs and chemical materials. In this paper, we focus on the family of smart polymer which is widely used in anticancer drugs manufacturing. In chemical graph theory, a topological index is a numerical representation of a chemical structure which correlates certain physico-chemical characteristics of underlying chemical compounds e.g., boiling point and melting point. More preciously, we focus on the family of smart polymer which is widely used in anticancer drugs manufacturing, and computed exact results for degree based topological indices.

Molecular graph serves as a convenient model for any real or abstract chemical compound. A topological index is the graph invariant number calculated from the graph representing the molecule. The advantage of topological indices is that it may be used directly as simple numerical descriptors in QSPR/QSAR models. Most of the topological descriptors are based either on atom-atom connectivity or on topological distances. A chemical reaction can be represented as the transformation of the chemical (Molecular) graph representing the reaction's substrate into another chemical graph representing the product. The type of chemical reaction where two substrates combine to form a single product (combination reaction) motivated us to study the effect of topological indices when a bridge is introduced between the respective vertices (of degree i, i=1, 2, 3) of two copies of the same graph. The graph obtained in this manner may or may not exist in reality, but it is the interest of the chemist to check the stability of the so obtained structure of the product. In this paper we present an algorithm to calculate the distance matrix of the resultant graph obtained after each iteration and thereby tabulate various topological indices. We also give the explicit formula for calculating Wiener index of the graph representing the resulting product.