Connective Eccentric Index of Circumcoronene Homologous Series of Benzenoid Hk

Let G be a molecular graph, a topological index is a numeric quantity related to G which is invariant under graph automorphisms. The eccentric connectivity index ξ(G) is defined as ξ(G) = ∑vV(G) d x ε(v) where dv, ε(v) denote the degree of vertex v in G and the largest distance between vand any other vertex u of G. The connective eccentric index of graph G is defined as Cξ(G) = ∑vV(G) dv /ε(v) In the present paper we compute the connective eccentric index of CircumcoroneneHomologous Series of Benzenoid Hk (k ≥ 1).

Computing eccentric connectivity index of nanostar dendrimers

Acta Chimica Slovaca ◽

10.1515/acs-2017-0017 ◽

2017 ◽

Vol 10 (2) ◽

pp. 96-100 ◽

Author(s):

Sara Mehdipour ◽

Mehdi Alaeiyan ◽

Ali Nejati

Keyword(s):

Molecular Graph ◽

Connectivity Index ◽

AbstractLet G be a molecular graph, the eccentric connectivity index of G is defined as ξc(G) = Σu∈V(G)deg(u)·ecc(u), where deg(u) denotes the degree of vertex u and ecc(u) is the largest distance between u and any other vertex v of G, namely, eccentricity of u. In this study, we present exact expressions for the eccentric connectivity index of two infinite classes of nanostar dendrimers.

Physical-chemical properties studying of molecular structures via topological index calculating

Open Physics ◽

10.1515/phys-2017-0029 ◽

2017 ◽

Vol 15 (1) ◽

pp. 261-269

Author(s):

Jianzhang Wu ◽

Mohammad Reza Farahani ◽

Xiao Yu ◽

Wei Gao

Keyword(s):

Topological Index ◽

Chemical Properties ◽

Molecular Structures ◽

Connectivity Index ◽

Chemical Characteristics ◽

Distance Computation ◽

Physical Chemical ◽

Mathematical Derivation ◽

Mathematical Standpoint

AbstractIt’s revealed from the earlier researches that many physical-chemical properties depend heavily on the structure of corresponding moleculars. This fact provides us an approach to measure the physical-chemical characteristics of substances and materials. In our article, we report the eccentricity related indices of certain important molecular structures from mathematical standpoint. The eccentricity version indices of nanostar dendrimers are determined and the reverse eccentric connectivity index for V-phenylenic nanotorus is discussed. The conclusions we obtained mainly use the trick of distance computation and mathematical derivation, and the results can be applied in physics engineering.

Connective Eccentric Index of an Infinite Family of Linear Polycene Parallelogram Benzenoid

International Letters of Chemistry Physics and Astronomy ◽

10.18052/www.scipress.com/ilcpa.37.57 ◽

2014 ◽

Vol 37 ◽

pp. 57-62

Author(s):

Mohammad Reza Farahani

Keyword(s):

Infinite Family ◽

Connectivity Index ◽

Maximal Path ◽

Molecular Graphs ◽

Let G=(V, E) be a graph, where V(G) is a non-empty set of vertices and E(G) is a set of edges.We defined dv denote the degree of vertex v∈V(G). The Eccentric Connectivity index ξ(G) and theConnective Eccentric index Cξ(G) of graph G are defined as ξ(G)= ∑ v∈V(G)dv x ξ(v) and Cξ(G)=ξ(G)= ∑ v∈V(G)dv x ξ(v)- where ε(v) is defined as the length of a maximal path connecting a vertex v toanother vertex of G. In this present paper, we compute these Eccentric indices for an infinite family oflinear polycene parallelogram benzenod by a new method.Keywords: Molecular graphs; Linear polycene parallelogram; Benzenoid; Eccentric connectivityindex; Connective eccentric index

Fourth Atom-Bond Connectivity Index of an Infinite Class of Nanostar Dendrimer D3[n]

JOURNAL OF ADVANCES IN CHEMISTRY ◽

10.24297/jac.v12i8.2838 ◽

2016 ◽

Vol 12 (8) ◽

pp. 301-305

Author(s):

Mohammad Reza Farahani

Keyword(s):

Topological Index ◽

Connectivity Index ◽

Infinite Class ◽

Degree Of Vertex ◽

Abc Index ◽

Atom Bond

The atom-bond connectivity (ABC) index of a graph G is a connectivity topological index was defined as where dv denotes the degree of vertex v of G. In 2010, M. Ghorbani et. al. introduced a new version of atom-bond connectivity index as where In this paper, we compute a cloused formula of ABC4 index of an infinite class of Nanostar Dendrimer D3[n]. A Dendrimer is an artificially manufactured or synthesized molecule built up from branched units called monomers.

New Definition of Atomic Bond Connectivity Index to Overcome Deficiency of Structure Sensitivity and Abruptness in Existing Definition

Scientific Inquiry and Review ◽

10.32350/sir.34.01 ◽

2019 ◽

Vol 3 (4) ◽

pp. 1-20 ◽

Author(s):

Abaid ur Rehman Virk ◽

M. A. Rehman ◽

Waqas Nazeer

Keyword(s):

Topological Index ◽

Molecular Graph ◽

Structure Sensitivity ◽

Connectivity Index ◽

Smoothness Property ◽

Silicon Carbides ◽

Abc Index ◽

Definition Of

Topological Index (TI) is a numerical value associated with the molecular graph of the compound. Smoothness property states that a TI is good if its Structure Sensitivity (SS) is as large as possible and its Abruptness (Abr) is small. In 2013, Gutman proved that Atomic Bond Connectivity (ABC) index has small SS and high Abr. In this paper, we defined reverse Atomic Bond Connectivity (ABC) index to overcome this problem. Moreover, we computed reverse ABC index for Silicon Carbides, Bismith Tri-Iodide and Dendrimers.

The eccentric version of atom-bond connectivity index of tetra sheet networks

Discrete Mathematics Algorithms and Applications ◽

10.1142/s1793830918500659 ◽

2018 ◽

Vol 10 (05) ◽

pp. 1850065 ◽

Author(s):

Muhammad Imran ◽

Abdul Qudair Baig ◽

Muhammad Razwan Azhar

Keyword(s):

Connected Graph ◽

Molecular Graph ◽

Theoretical Chemistry ◽

Connectivity Index ◽

Maximum Distance ◽

Topological Descriptor ◽

Degree Of A Vertex ◽

Connectivity Indices ◽

Atom Bond

Among topological descriptor of graphs, the connectivity indices are very important and they have a prominent role in theoretical chemistry. The atom-bond connectivity index of a connected graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] represents the degree of a vertex [Formula: see text] of [Formula: see text] and the eccentric connectivity index of the molecular graph [Formula: see text] is represented as [Formula: see text], where [Formula: see text] is the maximum distance between the vertex [Formula: see text] and any other vertex [Formula: see text] of the graph [Formula: see text]. The new eccentric atom-bond connectivity index of any connected graph [Formula: see text] is defined as [Formula: see text]. In this paper, we compute the new eccentric atom-bond connectivity index for infinite families of tetra sheets equilateral triangular and rectangular networks.

Choosing the exponent in the definition of the connectivity index

Journal of the Serbian Chemical Society ◽

10.2298/jsc0109605g ◽

2001 ◽

Vol 66 (9) ◽

pp. 605-611 ◽

Cited By ~ 13

Author(s):

Ivan Gutman ◽

Mirko Lepovic

Keyword(s):

Carbon Atom ◽

Topological Index ◽

Organic Molecules ◽

Molecular Graph ◽

Chemical Properties ◽

Connectivity Index ◽

Physico Chemical ◽

Definition Of ◽

Molecular Branching ◽

Suitable Measure

Let ?v denote the degree of the vertex v of a molecular graph G. Then the connectivity index of G is defined as C (?) = G (?,C) = ? (?u?v)?, where the summation goes over all pairs of adjacent vertices. The exponent ? is usually chosen to be equal to -1/2, but other options were considered as well, especially ?=-1. We show that whereas C(-1/2) is a suitable measure of branching of the carbon-atom skeleton of organic molecules, and thus applicable as a topological index for modeling physico-chemical properties of the respective compounds, this is not the case with C(-1). The value of ? is established, beyond which C(?) fails to correctly reflect molecular branching.

Eccentric topological properties of a graph associated to a finite dimensional vector space

Main Group Metal Chemistry ◽

10.1515/mgmc-2020-0020 ◽

2020 ◽

Vol 43 (1) ◽

pp. 164-176

Author(s):

Jia-Bao Liu ◽

Imran Khalid ◽

Mohammad Tariq Rahim ◽

Masood Ur Rehman ◽

Faisal Ali ◽

...

Keyword(s):

Vector Space ◽

Topological Index ◽

Topological Indices ◽

Connectivity Index ◽

Dimensional Vector ◽

Dimensional Vector Space ◽

Eccentricity Index ◽

Finite Dimensional Vector Space ◽

Finite Dimensional

AbstractA topological index is actually designed by transforming a chemical structure into a number. Topological index is a graph invariant which characterizes the topology of the graph and remains invariant under graph automorphism. Eccentricity based topological indices are of great importance and play a vital role in chemical graph theory. In this article, we consider a graph (non-zero component graph) associated to a finite dimensional vector space over a finite filed in the context of the following eleven eccentricity based topological indices: total eccentricity index; average eccentricity index; eccentric connectivity index; eccentric distance sum index; adjacent distance sum index; connective eccentricity index; geometric arithmetic index; atom bond connectivity index; and three versions of Zagreb indices. Relationship of the investigated indices and their dependency with respect to the involved parameters are also visualized by evaluating them numerically and by plotting their results.

Eccentric Connectivity Index of Molecular Grapgs of Chemical Trees with Application to Alkynes

Journal of Computational and Theoretical Nanoscience ◽

10.1166/jctn.2016.5615 ◽

2016 ◽

Vol 13 (10) ◽

pp. 6694-6697 ◽

Author(s):

R. S Haoer ◽

K. A Atan ◽

A. M Khalaf ◽

M. R. Md Said ◽

R Hasni

Keyword(s):

Molecular Structure ◽

Mathematical Modelling ◽

Biological Activities ◽

Molecular Graph ◽

Connectivity Index ◽

Chemical Bonds ◽

Degree Of A Vertex ◽

Structure Descriptor ◽

Chemical Trees

Let G = (V,E) be a simple connected molecular graph. The eccentric connectivity index ξ(G) is a distance–based molecular structure descriptor that was recently used for mathematical modelling of biological activities of diverse nature. In such a simple molecular graph, vertices represent atoms and edges represent chemical bonds, we denoted the sets of vertices and edges by V = V(G) and E = E(G), respectively. If d(u,v) be the notation of distance between vertices u,v ∈ V and is defined as the length of a shortest path connecting them. Then, the eccentricity connectivity index of a molecular graph Gis defined as ξ(G) = Σv∈V(G) deg(V)ec(V), where deg(V) (or simply dv) is degree of a vertex V ∈ V(G), and is defined as the number of adjacent vertices with V. ec(V) is defined as the length of a maximal path connecting to another vertex of v. In this paper, we establish the general formulas for the eccentricity connectivity index of molecular graphs classes of chemical trees with application to alkynes.

The eccentric connectivity index of armchair polyhex nanotubes

Macedonian Journal of Chemistry and Chemical Engineering ◽

10.20450/mjcce.2010.175 ◽

2010 ◽

Vol 29 (1) ◽

pp. 71 ◽

Cited By ~ 8

Author(s):

Mahboubeh Saheli ◽

Ali Reza Ashrafi

Keyword(s):

Exact Expression ◽

Connectivity Index ◽

The eccentric connectivity index ξ(G) of the graph G is defined as ξ(G) = Σu∈V(G) deg(u)ε(u) where deg(u) denotes the degree of vertex u and ε(u) is the largest distance between u and any other vertex v of G. In this paper an exact expression for the eccentric connectivity index of an armchair polyhex nanotube is given.