Total Eccentricity Research Articles

Distance and Degree Based Topological Indices of Cog-Wheel Graph, n-Barbell Graph and Boron Kagome Lattice

Abstract Let G = (V, E), be a graph with vertex and edge set, say V(G) and E(G). In chemical graphs the vertices and edges of the graphs represents atoms and chemical bond of the molecule. Since the distance based topological indices having high degree of predictability of pharmacological properties. In this paper we compute Eccentricity connectivity polynomial, Total eccentricity polynomial of Barbell graph and Cog wheel graph and degree based topological indices of Boron kagome lattice chemical structure.

On the Non-Commuting Graph of the Group U6n

Let G be a finite group. The non-commuting graph of G is a simple graph Γ(G) whose vertices are elements of G∖Z(G), where Z(G) is the center of G, and two distinct vertices a and b are joint by an edge if ab≠ba. In this paper, we study the non-commuting graph of the group U6n. The independent number, clique and chromatic numbers of the non-commuting graph of the group U6n, Γ(U6n), are determined. Additionally, the resolving polynomial, total eccentricity and independent polynomials of Γ(U6n) are computed. Finally, the detour and eccentric connectivity indices of Γ(U6n) are found.

Study for Some Eccentricity-based Topological Indices of Second Type of Dominating David-derived Network.

Dominating David-derived networks are widely studied due to their fractal nature, with applications in topology, chemistry, and computer sciences. The use of molecular structure descriptors is a standard procedure that is used to correlate the biological activity of molecules with their chemical structures, which can be useful in the field of pharmacology. This article's goal is to develop analytically closed computing formulas for eccentricitybased descriptors of the second type of dominating David-derived network. Thermodynamic characteristics, physicochemical properties, and chemical and biological activities of chemical graphs are just a few of the many properties that may be determined using these computation formulas. Vertex sets were initially divided according to their degrees, eccentricities, and cardinalities of occurrence. The eccentricity-based indices are then computed using some combinatorics and these partitions. Total eccentricity, average eccentricity, and the Zagreb index are distance-based topological indices utilized in this study for the second type of dominating David-derived network, denoted as D2(m). These calculations will assist the readers in estimating the fractal and difficult-tohandle thermodynamic and physicochemical aspects of chemical structure. Apart from configuration and impact resistance, the D2(m) design has been used for fundamental reasons in a variety of technical and scientific advancements.

On some topological indices of zero divisor graphs of direct product of three finite fields

In this paper, we determine some degree-based topological indices, such as the Sombor index, the first and second Zagreb indices, the forgotten topological index, the Narumi–Katayama index, the first and second multiplicative Zagreb indices, the atom-bond connectivity index, and eccentricity-based topological indices such as total eccentricity, the first and second Zagreb eccentricity indices, and the eccentricity connectivity index of the zero divisor graph with vertex set non-zero zero divisors of the reduced ring of the direct product of three finite fields.

Eccentricity-based topological indices of hexagonal networks

ABSTRACT Chemical graph theory acts as a tool for converting molecular information to a numerical parameter. Topological indices are numeric quantities that are related to the physio-chemical properties of chemical compounds. Distance- and Degree-based topological indices and Counting-related polynomials are three prominent and extensively researched classes of topological indices. In all these categories, distance-based topological descriptors have a significant impact on chemical graph theory. In this paper, the ‘Total eccentricity index ζ ( G ) , the Geometric-arithmetic index G A 4 ( G ) , Eccentricity-based Zagreb indices M 1 ∗ ( G ) , M 1 ∗ ∗ ( G ) and M 2 ∗ ( G ) , the Average eccentricity index a v e c ( G ) and the Atom-bond connectivity index A B C 5 ( G ) ’ of hexagonal networks are computed.

Distance-based graphical indices for predicting thermodynamic properties of benzenoid hydrocarbons with applications

This paper considers all the commonly occurring distance-related graphical indices and investigates their potential to predict thermodynamic properties of benzenoid hydrocarbons (BHs). Customarily, the entropy So and the heat capacity Cp have been chosen to be the representatives of thermodynamic characteristics. For test molecules, the lower 30 BHs have been opted and it is justified because the experimental data of both Cp and So is publicly available and the number 30 is sufficiently large enough to validate statistical inferences. In this paper, firstly, we propose a computer-dependent computational method to compute all distance-related (including eccentricity-related as well as valency-distance-related indices) of chemical graphs. The computational technique is employed further to evaluate the distance-related topological indices available in the literature. The statistical inferences suggested certain unexpected results as the less-studied distance descriptors such as the second atom-bond connectivity (ABC2) index, the total eccentricity (ζ) index, and the eccentric-connectivity (ξ) index outperform the well-researched descriptors such as the Szeged (Sz), the Wiener W, the Padmakar-Ivan (PI) indices generate poor correlation power. Among the best descriptors for correlating thermodynamic characteristics of BHs, only the ABC2 index showcases the mean correlation coefficient ρ>0.95 which is the minimum threshold for application of a descriptor in structure–property as well as structure–activity (QSPR/QSAR) modeling. The five best distance descriptors are then employed in detailed statistical analysis and most appropriate regression models suggested by the data are non-linear. The applications of the analysis are presented in correlation of the entropy So and the heat capacity Cp of linear polyacenes.

Study of eccentricity based topological indices for benzenoid structure

Topological indices play paramount role in defining chemical and structural properties of different compounds. Chemical graph theory is useful for predicting the bioactivity and physicochemical properties through numerical invariants. A broad range of topological indices are studied and used in theoretical chemistry. The eccentricity of a graph is maximum distance from one vertex a to another vertex b. The connectivity based topological indices depict vital role in mathematical chemistry. In this paper, we discuss Benzenoid Hourglass Network and calculate its total eccentricity, average eccentricity, atom-bond connectivity index, eccentricity based Zagreb index and geometric-arithmetic index. Some new helpful closed formulas are developed.

Physio-chemical properties of HCP ( U ) and HEX ( U ) crystal structure lattice via eccentricity dependent chemical invariants

A crystal lattice is the three-dimensional structural arrangement of atoms or molecules inside a crystalline solid as points. Each crystal lattice consists of repeating unit cells in different directions. From earlier scientific research, it was recognised that the physio-chemical properties of any crystal structure lattice are highly reliant on the molecular structure of the network. This study led us to investigate complex structures through a mathematical perspective using a chemical invariant (topological index) by a chemical graph theory that correlates a chemical graph structure and physio-chemical properties, where atoms represent the nodes and a bond between atoms is considered as an edge. In this research, we have given explicit expressions for eccentricity-based chemical invariants, namely, eccentric connectivity (EC), total eccentricity (TE), eccentricity-based Zagreb (EZ) and connective eccentric (CE) for inorganic symmetrical Hexagonal Close-Packed and Hexagonal ( crystal structure lattices.

Comparative Study of Prism Octahedron Network via Eccentric Invariants

Topological indices are empirical features of graphs that characterize the topology of the graph and, for the most part, are graph independent. An important branch of graph theory is chemical graph theory. In chemical graph theory, the atoms corresponds vertices and edges corresponds covalent bonds. A topological index is a numeric number that represents the topology of underline structure. In this article, we examined the topological properties of prism octahedron network of dimension m and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to utilize the distance between the vertices of a prism octahedron network.

Applications on Topological Indices of Zero-Divisor Graph Associated with Commutative Rings

A topological index is a numeric quantity associated with a chemical structure that attempts to link the chemical structure to various physicochemical properties, chemical reactivity, or biological activity. Let R be a commutative ring with identity, and Z*(R) is the set of all non-zero zero divisors of R. Then, Γ(R) is said to be a zero-divisor graph if and only if a·b=0, where a,b∈V(Γ(R))=Z*(R) and (a,b)∈E(Γ(R)). We define a∼b if a·b=0 or a=b. Then, ∼ is always reflexive and symmetric, but ∼ is usually not transitive. Then, Γ(R) is a symmetric structure measured by the ∼ in commutative rings. Here, we will draw the zero-divisor graph from commutative rings and discuss topological indices for a zero-divisor graph by vertex eccentricity. In this paper, we will compute the total eccentricity index, eccentric connectivity index, connective eccentric index, eccentricity based on the first and second Zagreb indices, Ediz eccentric connectivity index, and augmented eccentric connectivity index for the zero-divisor graph associated with commutative rings. These will help us understand the characteristics of various symmetric physical structures of finite commutative rings.

Total eccentricity index of graphs with fixed number of pendant or cut vertices

The total eccentricity index of a connected graph is defined as sum of the eccentricities of all its vertices. In this paper, we give the sharp upper bound on the total eccentricity index over graphs with fixed number of pendant vertices and the sharp lower bound on the same over graphs with fixed number of cut vertices. We also provide the sharp upper bounds on the total eccentricity index over graphs with s cut vertices for \(s=0, 1, n-3, n-2\) and propose a conjecture for \(2\le s\le n-4\).

Comparative Study of Planar Octahedron Molecular Structure via Eccentric Invariants

A branch of graph theory that makes use of a molecular graph is called chemical graph theory. Chemical graph theory is used to depict a chemical molecule. A graph is connected if there is an edge between every pair of vertices. A topological index is a numerical value related to the chemical structure that claims to show a relationship between chemical structure and various physicochemical attributes, chemical reactivity, or, you could say, biological activity. In this article, we examined the topological properties of a planar octahedron network of m dimensions and computed the total eccentricity, average eccentricity, Zagreb eccentricity, geometric arithmetic eccentricity, and atom bond connectivity eccentricity indices, which are used to determine the distance between the vertices of a planar octahedron network.

On eccentricity-based topological indices of line and para-line graphs of some convex polytopes

Graph theory has been studied different areas such as mathematics, information and chemistry sciences. It is about descriptors in quantitative structure property relationship (QSPR) and quantitative structure activity relationship (QSAR) studies in the chemical network. Let G = (V(G), E(G)) be a graph without directed and multiple edges and without loops. A lot of topological indices have been defined for QSPR/QSAR studies. There are several types of these indices such as degree-based indices, eccentricity-based indices, and so on. The eccentricity-based topological indices are very important QSPR/QSAR studies, also recently these indices have been studied in many papers. In this paper, some eccentricity-based topological indices namely the connective eccentricity index xce(G), the eccentric connectivity index xc(G), the modified eccentric connectivity index xc(G), the total eccentricity index x(G), the Zagreb eccentricity indices M*1(G), M**1(G), M*2(G), the average eccentricity index avec(G), the eccentricity based geometric-arithmetic index GA4(G) and new version of ABC index such as ABC5(G) have been computed for line and para-line graphs of some convex polytopes Dn, Qn and Rn which are geometric graphs.

Eccentricity-Based Topological Descriptors of First Type of Hex-Derived Network

Graph theory has made significant progress in mathematical chemistry and has gained a lot of traction among scientists due to its numerous applications in mathematical chemistry. The numerical invariants of a molecular structure are known as molecular topological descriptors, and they are highly effective for predicting their bioactivity. A number of such indices are examined and applied in pharmaceutical research, chemistry, medication development, and other fields. The eccentricity-based Zagreb indices, total eccentricity, geometric arithmetic G A 4 , atom-bond connectivity A B C 5 , and average eccentricity indices of a hex-derived network of first type are computed in this article. We also provide analytically closed formulas for these descriptors, which may be used to investigate the underlying topologies.

The Intersection Graph of Subgroups of the Dihedral Group of Order 2pq

For a finite group G, the intersection graph of G is the graph whose vertex set is the set of all proper non-trivial subgroups of G, where two distinct vertices are adjacent if their intersection is a non-trivial subgroup of G. In this article, we investigate the detour index, eccentric connectivity, and total eccentricity polynomials of the intersection graph of subgroups of the dihedral group for distinct primes . We also find the mean distance of the graph .

Computing Some Eccentricity-Based Topological Indices of Para-Line Graphs of Hexagonal Cactus Chains

Let be a simple molecular graph without directed and multiple edges and without loops. Graph theory has become an important component of the chemical mathematics, and it has become one of the most powerful mathematical tools in the analysis and study of the architecture of a chemical network. It studies of descriptors in quantitative structure-property relationship (QSPR) and quantitative structure-activity relationship (QSAR) studies in the chemistry science. There are a lot of topological indices in QSPR/QSAR studies. In this paper, some eccentricity-based topological indices namely the eccentric connectivity index the modified eccentric connectivity index the total eccentricity index the second Zagreb eccentricity index and the average eccentricity index are computed for the para-line graphs of some hexagonal cactus chains namely the para-chain the ortho-chain and the meta-chain

Total eccentricity index of trees with fixed pendent vertices and trees with fixed diameter

Total eccentricity index of trees with fixed pendent vertices and trees with fixed diameter

A note on eccentricity based topological indices of honeycomb, oxide and 2-power interconnection networks

In a series of papers, Imran et al. reported the total eccentricity index, the average eccentricity index, the eccentricity-based Zagreb indices, the atom-bond connectivity index, and the geometric arithmetic index of honeycomb networks, hypertrees, X-trees, and oxide networks. In this paper, it is demonstrated that these computations contain flaws. Corrected, and in many cases also simplified, formulas are also obtained.

Eccentricity-Based Topological Invariants of Dominating David-Derived Networks

A topological index is a numerical descriptor of the molecular structure based on certain topological features of the corresponding molecular graph. Topological indices are scientific contemplations of a graph that outline its subatomic topology and are graph-invariant. In a QSAR/QSPR study, topological indices are utilized to anticipate the physico-concoction resources and bioactivity of compounds. In this paper, we study some distance-based topological indices such as eccentric connectivity index (ECI), total eccentricity index (TEI), and eccentricity-based Zagreb index for dominating David-derived networks (DD network) and provide exact formulae of the said indices. These outcomes are valuable to organize the science of hidden topologies of this network.

Study of generalized networks using graph theory

We study eccentricity-based indices such as Zagreb eccentricity indices, general eccentricity index and total eccentricity index. We present exact values of eccentricity-based indices of generalized networks related to binary and $m$-ary trees, where $m \ge 2$.