Eccentric Connectivity 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.

Eccentric connectivity index in complementary prisms

The topological index is just one of several very useful tools that graph theory has made available to chemists. Topological indices are invariants of real numbers under graph isomorphisms. Several topological indices have been defined. Some of them are used to model chemical, pharmaceutical and other properties of molecules. The eccentric connectivity index (eci) is also a topological index. The eci of [Formula: see text], denoted by [Formula: see text], is defined as [Formula: see text], where [Formula: see text] represents the degree of a vertex [Formula: see text] and [Formula: see text] is its eccentricity. In this paper, exact formula for the eci of complementary prisms is derived.

Structure-property modeling of coumarins and coumarin-related compounds in pharmacotherapy of cancer by employing graphical topological indices.

Coumarins, a subgroup of colorless and crystalline oxygenated heterocyclic compounds originally discovered in the plant Dipteryx odorata, were the subject of a recent study investigating their quantitative structure-activity relationship (QSAR) in cancer pharmacotherapy. This study utilized graph theoretical molecular descriptors, also known as topological indices, as a numerical representation method for the chemical structures embedded in molecular graphs. These descriptors, derived from molecular graphs, play a pivotal role in quantitative structure-property relationship (QSPR) analysis. In this paper, intercorrelation between the Balban index, connective eccentric index, eccentricity connectivity index, harmonic index, hyper Zagreb index, first path Zagreb index, second path Zagreb index, Randic index, sum connectivity index, graph energy and Laplacian energy is studied on the set of molecular graphs of coumarins. It is found that the pairs of degree-based indices are highly intercorrelated. The use of these molecular descriptors in structure-boiling point modeling was analyzed. Finally, the curve-linear regression between considered molecular descriptors with physicochemical properties of coumarins and coumarin-related compounds is obtained.

Some sufficient conditions for graphs to be [formula omitted]-leaf-connected

Let G be a graph and S be a subset of V(G). A graph G is called S-leaf-connected if G has a spanning tree T such that S is the set of leaves of T. For k≥2, we say a graph G is k-leaf-connected if |V(G)|>k and given any subset S of V(G) with |S|=k, G is S-leaf-connected. In the present note, we give some sufficient conditions on eccentric connectivity index, eccentric distance sum, connective eccentricity index and difference of Zagreb indices for connected graphs to be k-leaf-connected. These results generalize the sufficient conditions on these indices for connected graphs to be Hamilton-connected. At last, we obtain a sufficient condition for a graph to be k-leaf-connected in terms of the general sum-connectivity index of the complement graph.

Some inequalities between degree- and distance-based topological indices

hefirst Zagreb indexM1and the second Zagreb indexM2belongto the class of degree-based topological indices which are defined fora simple connected graphGwith vertex setV={υ1,υ2,···,υn}asM1(G)=Pn ̇ı=1d2 ̇ıandM2(G)=Pυ ̇ı∼υ ̇jd ̇ıd ̇j,whered ̇ıis the degreeof vertexυiandυ ̇ı∼υ ̇jrepresents the adjacency of verticesυ ̇ıandυ ̇jinG. The eccentric connectivity index (ECI) is a distance basedtopological index, denoted byξc,isdefined asξc(G)=Pni=1ε ̇ıd ̇ı,whereε ̇ıis the eccentricity ofυ ̇ıinG. The aim of this paper is toderive the inequalities between ECI and the Zagreb indices. Moreover,we establish the inequalities between some variants of ECI and theZagreb indices

Topological Indices and Structural Properties of Cubic Power Graph of Dihedral Group

The cubic power graph of finite group G with identity element e, is an undirected finite, simple graph in which a pair of distinct vertices x, y have an edge iff xy = z3 or yx = z3 for any z ∈ Dn with z3 ≠ e. In this paper, we have studied the structural representation of the cubic power graph of the dihedral group and various structural properties such as clique, girth, vertex degree, chromatic number, independent number, matching number, perfect matching, dominating number, etc. We have also calculated various topological indices such as the Harary index, the first and second Zagreb indices, the Wiener and hyper-Wiener indices, the Schultz index, the harmonic index, the general Randic index, the eccentric connectivity index, the Gutman index, the atomic-bond connectivity index, and the geometricarithmetic index of the cubic power graph of dihedral group Dn when gcd(n, 3) = 1.

On Relations between Distance-Based Topological Indices

Motivated by the recent paper On topological indices and their reciprocals, MATCH Commun. Math. Comput. Chem. 91 (2024) 287, we establish additional relations between distance- and degree-and-distance-based molecular structure descriptors: Wiener, hyper-Wiener, Harary, connective eccentricity, eccentric connectivity, degree distance, Gutman, additively weighted Harary, and multiplicatively weighted Harary indices, especially for their products.

On Lanzhou Index of Graphs

Let G = ( V , E ) be a simple graph with vertex set V ( G ) and edge set E ( G ) . The Lanzhou index of a graph G is defined by L z ( G ) = ∑ u ∈ V ( G ) d 2 u ¯¯¯ d u , where d u ( ¯¯¯ d u resp.) denotes the degree of the vertex u in G ( ¯¯¯¯ G , the complement graph of G resp.). It has predictive powers to provide insights of chemical relevant properties of chemical graph structures. In this paper we discuss some properties of Lanzhou index. Several inequalities having lower and upper bound for the Lanzhou index in terms of first, second and third Zagreb indices, radius of graph, eccentric connectivity index, Schultz index, inverse sum indeg index and symmetric division deg index, are discussed. At the end the Lanzhou index of corona and join of graphs have been derived.

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.

On the Distance Spectrum and Distance-Based Topological Indices of Central Vertex-Edge Join of Three Graphs

In this paper, we introduce a new graph operation based on a central graph called central vertex-edge join (denoted by $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$) and then determine the distance spectrum of $G_{n_1}^C \triangleright (G_{n_2}^V\cup G_{n_3}^E)$ in terms of the adjacency spectra of regular graphs $G_1$, $G_2$ and $G_3$ when $G_1$ is triangle-free. As a consequence of this result, we construct new families of non-D-cospectral D-equienergetic graphs. Moreover, we determine bounds for the distance spectral radius and distance energy of the central vertex-edge join of three regular graphs. In addition, we provide its results related to graph invariants like eccentric-connectivity index, connective eccentricity index, total-eccentricity index, average eccentricity index, Zagreb eccentricity indices, eccentric geometric-arithmetic index, eccentric atom-bond connectivity index, Wiener index. Using these results, we calculate the topological indices of the organic compounds Methylcyclobutane $(C_5H_{10})$ and Spirohexane $(C_6H_{10})$.

Response of Embedded Plates in Reinforced Concrete Loaded in Eccentric Shear towards an Edge

Embedded plates (EPs) are commonly used to connect steel to reinforced concrete elements. Due to a lack of industry-wide standard designs, EPs are custom designed for every instance in each project. This leads to many inefficiencies in the construction process and introduces susceptibilities to error. North American design standards based on the concrete capacity design (CCD) philosophy require many assumptions to predict EP capacity, which then lead to inconsistencies in their application. CCD is also well suited for analysis as it depends on a considerable numbers of variables (e.g., edge distances, anchor size, number, and length) to check capacity. The sheer number of variables makes it difficult for designers to come up with a trial design to fit a situation. This study aims to improve the efficiency of this process by proposing standard EPs. A subset of these proposed standard EPs are then experimentally tested to verify predicted capacities and evaluate design assumptions using existing CCD approaches in North America. Four- and six-anchor proposed standard EPs with shear tab connections were placed at four distances from the concrete edge (75–250 mm) and tested in shear towards the edge. North American provisions for concrete anchorage were adequate in predicting the failure loads if connection eccentricity, caused by the gap between the shear tab bolt line and the exposed surface of the plate, is considered in capacity predictions. Mean test-to-predicted ratios of 0.92 and 1.05 were obtained, respectively, when not considering and considering this eccentricity. Rotations of these connections during testing (0.01 to 0.02 rad at peak load with further rotations post-peak) and signs of secondary tension breakout cones suggest that connection eccentricity significantly affects the behavior of EPs and should be considered in design.

Eccentric connectivity index in transformation graph Gxy+

Abstract Let G be a connected graph with vertex set V(G)and edge set E(G). The eccentric connectivity index of G is defined as ∑ ν ∈ V ( G ) ec ( ν ) deg ( ν ) \sum\limits_{\nu\in{\rm{V}}\left({\rm{G}}\right)}{{\rm{ec}}\left(\nu\right)\,{\rm{deg}}\left(\nu\right)} where ec(v) the eccentricity of a vertex v and deg(v)is its degree and denoted by ɛc(G). In this paper, we investigate the eccentric connectivity index of the transformation graph Gxy+.

Eccentric Connectivity Index of Nanosheets and Nanotube of SiO2

Chemical graph theory is a field related to Chemistry which is used to predict the behavior of chemical structures. The current trend in Chemical graph theory is evaluating topological indices. They are the numerical descriptors of the molecular structures derived from their corresponding molecular graph. These indices are studied and used in drugs, pharmaceutical research, and other fields. In this paper, the eccentric connectivity index is computed for nanosheets and nanotubes of SiO2.

Computational analysis for eccentric neighborhood Zagreb indices and their significance

In this paper, a novel eccentric neighborhood degree-based topological indices, termed eccentric neighborhood Zagreb indices, have been conceptualized and its discriminating power investigated with regard to the predictability of the boiling point of the chemical substances. The discriminating power of the eccentric neighborhood Zagreb indices was compared with that of Wiener and eccentric connectivity indices. Some explicit results for those new indices for some graphs and graph operations such as join, disjunction, composition, and symmetric difference.

Eccentricity Based Entropy Indices of Water Soluble Dendritic Unimolecular Polyether Micelle

Computation of Topological indices (TI) is useful in the analysis of the chemical as well as physical properties of different molecular structures. Among the TIs, the eccentricity connectivity index shows an effective role of estimating medicament properties. In our article, we computed eccentricity-based entropies (Eccentric-connectivity and Total eccentric-connectivity entropy) for the molecular structure of Water Soluble Dendritic Unimolecular Polyether Micelle.

Further study of eccentricity based indices for benzenoid hourglass network

Topological Indices are the mathematical estimate related to atomic graph that corresponds biological structure with several real properties and chemical activities. These indices are invariant of graph under graph isomorphism. If top(h1) and top(h2) denotes topological index h1 and h2 respectively then h1 approximately equal h2 which implies that top(h1) = top(h2). In biochemistry, chemical science, nano-medicine, biotechnology and many other science's distance based and eccentricity-connectivity(EC) based topological invariants of a network are beneficial in the study of structure-property relationships and structure-activity relationships. These indices help the chemist and pharmacist to overcome the shortage of laboratory and equipment. In this paper we calculate the formulas of eccentricity-connectivity descriptor(ECD) and their related polynomials, total eccentricity-connectivity(TEC) polynomial, augmented eccentricity-connectivity(AEC) descriptor and further the modified eccentricity-connectivity(MEC) descriptor with their related polynomials for hourglass benzenoid network.

QSPR Study and Distance-Based New Topological Descriptors of Some Drugs Used in the COVID-19 Treatment

In chemistry and medical sciences, it is essential to study the chemical, biological, clinical, and therapeutic aspects of pharmaceuticals. To save time and money, mathematical chemistry focuses on topological indices used in quantitative structure-property relationship (QSPR) models to predict the properties of chemical structures. The COVID-19 pandemic is widely recognized as the greatest life-threatening crisis facing modern medicine. Scientists have tested various antiviral drugs available to treat COVID-19 disease, and some have found that they help get rid of this viral infection. Antiviral drugs such as Arbidol, chloroquine, hydroxychloroquine, lopinavir, remdesivir, ritonavir, thalidomide, and theaflavin are used to treat COVID-19. In this paper, reformulated leap Zagreb indices are introduced. Then, the reformulated leap Zagreb indices, leap eccentric connectivity indices, and reformulated Zagreb connectivity indices of these antiviral drugs are calculated. Curvilinear and multilinear regression models predicting the physicochemical properties of these antiviral drugs in terms of proposed indices are obtained and analyzed. The findings and models of this study will shed light on new drug discoveries for the treatment of COVID-19.

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.

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.