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Copyright of Journal of Central European Agriculture is the property of Journal of Central European Agriculture and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Zagreb indices are one of the most extensively studied degree-based structural descriptors for analyzing various physicochemical properties of chemical compounds. In this paper, we define four new products of graphs based on adjacency relations and compute their Zagreb indices. Using these expressions we compute the Zagreb indices of various chemical compounds such as linear polyacene, a class of nanotubes NA2nm, toroidal fullerene NC2n2m(H2n2m) and hexagonal lattice. [ABSTRACT FROM AUTHOR]

Boron clusters are small, three-dimensional structures made of boron atoms. These come in a wide range of shapes and sizes, from basic planar constructions to complex polyhedral patterns. Boron clusters are fascinating from both a fundamental and practical perspective because of their unique electrical, optical, and chemical properties. More focus has lately been placed on boron cluster sheets, which are two-dimensional structures made of boron clusters. Quantitative structure-activity relationship (QSAR) studies implement M-polynomials, a type of molecular descriptor, to describe the topology of molecules. These are based on the notion of graph theory, which provides a theoretical framework for quantitatively studying molecular graphs. In this article, we discussed some novel topological descriptors-based M-polynomials and found algebraic formulations for the boron cluster or borophene sheets. We discussed first Zagreb, second Zagreb and Randić M-polynomials, based on the different differential and integral operators. [ABSTRACT FROM AUTHOR]

Graph theory serves as an engaging arena for the investigation of proof methods within the field of discrete mathematics, and its findings find practical utility in numerous scientific domains. Chemical graph theory is a specialized branch of mathematics that uses graphs to represent and analyze the structure and properties of chemical compounds. Topological indices are mathematical properties of graphs that play a crucial role in chemistry. They provide a unique way to connect the structural characteristics of chemical compounds to their corresponding molecular graphs. The flabellum graph F n (k , j) is obtained with the help of k ≥ 2 duplicates of the cycle graph C n with a common vertex (known as, central vertex). Then, in j of these duplicates, additional edges are added, joining the central vertex to all non-adjacent vertices. In this article, we compute different degree-based topological indices for flabellum graphs, including some well known indices, such as the Randić index, the atom bond connectivity index, the geometric–arithmetic index, and the Zagreb indices. This research provides an in-depth examination of these specific indices within the context of flabellum graphs. Moreover, the behavior of these indices is shown graphically, in terms of the parameters j , k , and n. Additionally, we have extended the concept of the first Zagreb index, to address the issue of cybercrime. This application enables us to identify criminals who exhibit higher levels of activity and engagement in multiple criminal activities when compared to their counterparts. Furthermore, we conducted a comprehensive comparative analysis of the first Zagreb index against the closeness centrality measure. This analysis sheds light on the effectiveness and relevance of the topological index in the context of cybercrime detection and network analysis. [ABSTRACT FROM AUTHOR]

The study of topological indices in graph theory is one of the more important topics, as the scientific development that occurred in the previous century had an important impact by linking it to many chemical and physical properties such as boiling point and melting point. So, our interest in this paper is to study many of the topological indices "generalized indices' network" for some graphs that have somewhat strange structure, so it is called the cog-graphs of special graphs "molecular network", by finding their polynomials based on vertex − edge degree then deriving them with respect to x , y , and x y , respectively, after substitution x = y = 1 of these special graphs are cog-path, cog-cycle, cog-star, cog-wheel, cog-fan, and cog-hand fan graphs; the importance of some types of these graphs is the fact that some vertices have degree four, which corresponds to the stability of some chemical compounds. These topological indices are first and second Zagreb, reduced first and second Zagreb, hyper Zagreb, forgotten, Albertson, and sigma indices. [ABSTRACT FROM AUTHOR]

Mathematical chemistry studies the chemical structure of molecules. Topological indices are numerical values which associates the chemical structure with the physical and chemical properties. Multiplicative Universal Zagreb indices are generalized degree-based topological indices which gave rise to several indices like first and second multiplicative, Zagreb and hyper-Zagreb indices, multiplicative sum and product conductivity indices. This research is designed to study the first and second multiplicative Universal Zagreb indices of carbon nanostructures (carbon nanosheet, nanotube and nanotorus) of the same chemical formula C 4 C 8. We also depict the values of first and second multiplicative, Zagreb and hyper-Zagreb indices as well as multiplicative sum and product connectivity indices for the mentioned structures. The graphical comparison for each of the multiplicative Zagreb indices is presented for all the carbon nanostructures with the same chemical formula C 4 C 8. [ABSTRACT FROM AUTHOR]

A novel graph polynomial, termed as vertex degree polynomial, has been conceptualized, and its discriminating power has been investigated regarding its coef-ficients and the coefficients of its derivatives and their relations with the physical and chemical properties of molecules. Correlation coefficients ranging from 95% to 98% were obtained using the coefficients of the first and second derivatives of this new polynomial. We also show the relations between this new graph polynomial, and two oldest Zagreb indices, namely the first and second Zagreb indices. We calculate the vertex degree polynomial along with its roots for some important families of graphs like tadpole graph, windmill graph, firefly graph, Sierpinski sieve graph and Kragujevac trees. Finally, we use the vertex degree polynomial to calculate the first and second Zagreb indices for the Dyck-56 network and also for the chemical compound triangular benzenoid G[r]. [ABSTRACT FROM AUTHOR]

Corona virus is a transforming and refastening pandemic that likely transmitting through an affected person in droplet-generated forms that have infected beyond 250 countries and threaten the whole world. There is no clear approach for taking care of corona cases. Besides, scientists around the world are working energetically to develop medicinal or anti-virus drugs. Scientists have developed the potency of Remdesivir to prevent corona virus in vitro. Topological indices are mathematical representations of a molecule developed by an algorithm executed to a given molecular description. Topological indices are used to design different physical, medical, chemical and biological properties of chemical compounds. The idea of line graph L (G) , for a graph G has found several applications in field of chemical research. In this paper, we present some reverse degree based topological indices namely, the reverse general randic index, the reverse atom bond connectivity index, the reverse geometric arithmetic index, the reverse forgotten index, the reverse balaban index and different types of Zagreb indices for the line graph of Remdesivir. The results attained can help in the design of new medicine for the treatment of corona virus. [ABSTRACT FROM AUTHOR]

The transition metal is a planar metallic organic structure, and tetra-cyano-benzene is one of the most studied networks of 3D series of transition metal. Tetra-cyano-benzene behaved as a useful object in the alloy synthesis industry due to its excellency of hardness. In spintronics, the tetra-cyano-benzene demonstrate a long-range ferromagnetic connection in the erection of magnetic, which is usually behaved as the ideal entrant. To study this novel tetra-cyano-benzene structure, we use an authentic mathematical tool known as vertex-edge and edge-vertex base topological indicators and shows some physical and chemical properties in numerical form, to understand the structure deeply. In this paper, we consider the formulas of the Zagreb indicator, first Zagreb alpha indicator, first Zagreb beta indicator, second Zagreb indicator, Randic indicators, Atom bond connectivity indicator, Geometric arithmetic indicator, Harmonic indicator and Sum connectivity indicator for transition metal tetra-cyano benzene (TCB (r , s)) structure based on vertex-edge and edge-vertex degree. [ABSTRACT FROM AUTHOR]

Topological indices are used to predict the physical properties of chemical compounds. It is an efficient technique in avoiding expensive and long laboratory experiments. For this, we computed the weighted degree and weighted edge‐based topological indices and developed a quantitative structure–property relationship between these entropy indices and the scaling physical properties of benzene derivatives. We developed a Maple based algorithm to compute these indices and the correlation between topological indices and physical properties have been developed with the software SPSS. Our study reveals that the redefined third Zagreb entropy ENTReZG3 is the most significant parameter and has good prediction ability for the physical properties boiling point and molecular weight. [ABSTRACT FROM AUTHOR]

In the fields of mathematical chemistry, a topological index, also known as a connectivity index, is a type of a molecular descriptor that is calculated based on the molecular graph of a chemical compound. Topological indices are an analytical framework of a graph which portray its topology and are mostly equal graphs. Topological indices (TIs) are numeral quantities that are used to foresee the natural correlation among the physicochemical properties of the chemical compounds in their fundamental network. TIs show an essential role in the theoretical abstract and environmental chemistry and pharmacology. In this paper, we compute many latest developed degree-based TIs. An analogy among the computed different versions of the TIs with the help of the numerical values and their graphs is also included.In this article, we compute the first Zagreb index, second Zagreb index, hyper Zagreb index, ABC Index, GA Index, and first Zagreb polynomial and second Zagreb polynomial of chemical graphs polythiophene, nylon 6,6, and the backbone structure of DNA. [ABSTRACT FROM AUTHOR]

A topological index (TI) is a numerical descriptor of a molecule structure or graph that predicts its different physical, biological, and chemical properties in a theoretical way avoiding the difficult and costly procedures of chemical labs. In this paper, for two connected (molecular) graphs G 1 and G 2 , we define the generalized total-sum graph consisting of various (molecular) polygonal chains by the lexicographic product of the graphs T k G 1 and G 2 , where T k G 1 is obtained by applying the generalized total operation T k on G 1 with k ≥ 1 as some integral value. Moreover, we compute the different degree-based TIs such as first Zagreb, second Zagreb, forgotten Zagreb, and hyper-Zagreb. In the end, a comparison among all the aforesaid TIs is also conducted with the help of certain statistical tools for some particular families of generalized total-sum graphs under lexicographic product. [ABSTRACT FROM AUTHOR]

Topological index is a useful number associated with molecular graph and the number correlate certain physico-chemical properties of chemical compounds. The concept of line graph and subdivision graph for a graph G has found various applications in chemical research. In this paper, we compute the first, second, and third Zagreb coindices, the F-coindex, the first and second multiplicative Zagreb coindices and the hyper Zagreb coindex of the subdivision graph and the line graph of subdivision graph of the wheel graph. [ABSTRACT FROM AUTHOR]

Neural networks in which communication works only among the neighboring units are called cellular neural networks (CNNs). These are used in analyzing 3D surfaces, image processing, modeling biological vision, and reducing nonvisual problems of geometric maps and sensory-motor organs. Topological indices (TIs) are mathematical models of the (molecular) networks or structures which are presented in the form of numerical values, constitutional formulas, or numerical functions. These models predict the various chemical or structural properties of the under-study networks. We now consider analogous graph invariants, based on the second connection number of vertices, called Zagreb connection indices. The main objective of this paper is to compute these connection indices for the cellular neural networks (CNNs). In order to find their efficiency, a comparison among the obtained indices of CNN is also performed in the form of numerical tables and 3D plots. [ABSTRACT FROM AUTHOR]

In predicting of their bioactivity and physicochemical properties of a chemical graph extremely important correlated with mathematical invariants in the topological indices. These topological indices are well-known in mathematical chemistry, drugs delivery, biology, gene therapy, nanotechnology and in other areas of applied sciences. In this paper, we study two families of Polyphenylene dendrimers, namely D1[n] and D2[n]. We also compute their topological indices, Zagreb indices and Zagreb coindices based on the concept of the line graphs. Furthermore, we analyze the results of these indices for graphs D1[n] and D2[n]. [ABSTRACT FROM AUTHOR]

A topological index is a numerical value associated with chemical constitution for correlation of chemical structure with various physical properties and chemical reactivity. It is calculated from a graph representing a molecule. Meanwhile, the non-commuting graph, Γ G of G, is defined as a graph of vertex set whose vertices are non-central elements and two distinct vertices are joined by an edge if and only if they do not commute. The main objective of this article is to determine the general formula of some topological indices, namely Wiener index, first Zagreb index and second Zagreb index for the non-commuting graph associated with generalised quaternion group in terms of n. [ABSTRACT FROM AUTHOR]

Network theory as an important role in the field of electronic and electrical engineering, for example, in signal processing, networking, communication theory, etc. The branch of mathematics known as Graph theory found remarkable applications in this area of study. A topological index (TI) is a real number attached with graph networks and correlates the chemical networks with many physical and chemical properties and chemical reactivity. The Optical Transpose Interconnection System (OTIS) network has received considerable attention in recent years and has a special place among real world architectures for parallel and distributed systems. In this report, we compute redefined first, second and third Zagreb indices of OTIS swapped and OTIS biswapped networks. We also compute some Zagreb polynomials of understudy Networks. [ABSTRACT FROM AUTHOR]

In the fields of chemical graph theory, topological index is a type of a molecular descriptor that is calculated based on the graph of a chemical compound. Topological indices help us collect information about algebraic graphs and give us mathematical approach to understand the properties of algebraic structures. With the help of topological indices, we can guess the properties of chemical compounds without performing experiments in wet lab. There are more than 148 topological indices in the literature, but none of them completely give all properties of under study compounds. Together, they do it to some extent; hence, there is always room to introduce new indices. In this paper, we present first and second reserve Zagreb indices and first reverse hyper-Zagreb indices, reverse GA index, and reverse atomic bond connectivity index for the crystallographic structure of molecules. We also present first and second reverse Zagreb polynomials and first and second reverse hyper-Zagreb polynomials for the crystallographic structure of molecules. [ABSTRACT FROM AUTHOR]

Topological index (numeric number) is a mathematical coding of the molecular graphs that predicts the physicochemical, biological, toxicological, and structural properties of the chemical compounds that are directly associated with the molecular graphs. The Zagreb connection indices are one of the TIs of the molecular graphs depending upon the connection number (degree of vertices at distance two) appeared in 1972 to compute the total electron energy of the alternant hydrocarbons. But after that, for a long period, these are not studied by researchers. Recently, Ali and Trinajstic Mol. Inform. 37 2018 , 1 − 7 restudied the Zagreb connection indices and reported that the Zagreb connection indices comparatively to the classical Zagreb indices provide the better absolute value of the correlation coefficient for the thirteen physicochemical properties of the octane isomers (all these tested values have been taken from the website http://www.moleculardescriptors.eu). In this paper, we compute the general results in the form of exact formulae & upper bounds of the second Zagreb connection index and modified first Zagreb connection index for the resultant graphs which are obtained by applying operations of corona, Cartesian, and lexicographic product. At the end, some applications of the obtained results for particular chemical structures such as alkanes, cycloalkanes, linear polynomial chain, carbon nanotubes, fence, and closed fence are presented. In addition, a comparison between exact and computed values of the aforesaid Zagreb indices is also included. [ABSTRACT FROM AUTHOR]

The concepts of geometric–arithmetic and harmonic indices were introduced in the area of chemical graph theory recently. They have proven to correlate well with physical and chemical properties of some molecules. The aim of this paper is to obtain new inequalities involving the first Zagreb, the harmonic, and the geometric–arithmetic G A 1 indices. Furthermore, inequalities relating these indices and line graphs are proven. [ABSTRACT FROM AUTHOR]

The algebraic study of graph matrices is an important area of Graph Theory giving information about the chemical and physical properties of the corresponding molecular structure. In this paper, we deal with the edge-Zagreb matrices defined by means of Zagreb indices which are the most frequently used graph indices. [ABSTRACT FROM AUTHOR]

M-polynomial of different molecular structures helps to calculate many topological indices. A topological index of graph G is a numerical parameter related to G which characterizes its molecular topology and is usually graph invariant. In the field of quantitative structure-activity (QSAR), quantitative structure-activity structure-property (QSPR) research, theoretical properties of the chemical compounds and their molecular topological indices such as the Zagreb indices, Randic index, Symmetric division index, Harmonic index, Inverse sum index, Augmented Zagreb index, multiple Zagreb indices etc. are correlated. In this report, we compute closed forms of M-polynomial, first Zagreb polynomial and second Zagreb polynomial of octagonal network. From the M-polynomial we recover some degree-based topological indices for octagonal network. [ABSTRACT FROM AUTHOR]

Copyright of Glasnik Zastite Bilja is the property of Zadruzna Stampa D.D. and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The topological indices are numerical invariants associated to a graph which describe its molecular topology. In QSAR/QSPR study, the Zagreb indices and Zagreb polynomials are used to predict the bioactivity of different chemical compounds. They also correlate the certain physicochemical properties of the chemical compounds. In this paper, we compute the closed formulas of the first and second Zagreb indices and their variants and their Zagreb polynomials for the two classes of perylenediimide-cored (PDI-cored) dendrimers. [ABSTRACT FROM AUTHOR]

In the studies of quantitative structure–activity relationships (QSARs) and quantitative structure–property relationships (QSPRs), graph invariants are used to estimate the biological activities and properties of chemical compounds. In these studies, degree-based topological indices have a significant place among the other descriptors because of the ease of generation and the speed with which these computations can be accomplished. In this paper, we give the results related to the first, second, and third Zagreb indices, forgotten index, hyper Zagreb index, reduced first and second Zagreb indices, multiplicative Zagreb indices, redefined version of Zagreb indices, first reformulated Zagreb index, harmonic index, atom-bond connectivity index, geometric-arithmetic index, and reduced reciprocal Randić index of a new graph operation named as "subdivision vertex-edge join" of three graphs. [ABSTRACT FROM AUTHOR]

There are numeric numbers that define chemical descriptors that represent the entire structure of a graph, which contain a basic chemical structure. Of these, the main factors of topological indices are such that they are related to different physical chemical properties of primary chemical compounds. The biological activity of chemical compounds can be constructed by the help of topological indices. In theoretical chemistry, numerous chemical indices have been invented, such as the Zagreb index, the Randić index, the Wiener index, and many more. Hex-derived networks have an assortment of valuable applications in drug store, hardware, and systems administration. In this analysis, we compute the Forgotten index and Balaban index, and reclassified the Zagreb indices, A B C 4 index, and G A 5 index for the third type of hex-derived networks theoretically. [ABSTRACT FROM AUTHOR]