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

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.

scholarly journals Choosing the exponent in the definition of the connectivity index

2001 ◽  
Vol 66 (9) ◽  
pp. 605-611 ◽  
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.

scholarly journals Relating the ABC and harmonic indices

2014 ◽  
Vol 79 (5) ◽  
pp. 557-563 ◽  
Author(s):  
Ivan Gutman ◽  
Lingping Zhong ◽  
Kexiang Xu
Keyword(s):  
Molecular Structure ◽  
Topological Index ◽  
Molecular Graph ◽  
Vertex Degree ◽  
Harmonic Index ◽  
Abc Index ◽  
Atom Bond ◽  
Structure Descriptor

The atom-bond connectivity (ABC) index is a much-studied molecular structure descriptor, based on the degrees of the vertices of the molecular graph. Recently, another vertex-degree-based topological index - the harmonic index (H) - attracted attention and gained popularity. We show how ABC and H are related.

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

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.

scholarly journals Connective Eccentric Index of Circumcoronene Homologous Series of Benzenoid Hk

2014 ◽  
Vol 32 ◽  
pp. 71-76
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Homologous Series ◽  
Topological Index ◽  
Molecular Graph ◽  
Connectivity Index ◽  
Eccentric Connectivity Index ◽  
Degree Of Vertex

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).

scholarly journals Minimum Variable Connectivity Index of Trees of a Fixed Order

2020 ◽  
Vol 2020 ◽  
pp. 1-4
Author(s):  
Shamaila Yousaf ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali
Keyword(s):  
Real Number ◽  
Topological Index ◽  
Nonnegative Real Number ◽  
Point Of View ◽  
Connectivity Index ◽  
Star Graph ◽  
Arbitrary Vertex ◽  
Mathematical Properties ◽  
Fixed Order ◽  
Definition Of

The connectivity index, introduced by the chemist Milan Randić in 1975, is one of the topological indices with many applications. In the first quarter of 1990s, Randić proposed the variable connectivity index by extending the definition of the connectivity index. The variable connectivity index for graph G is defined as ∑vw∈EGdv+γdw+γ−1/2, where γ is a nonnegative real number, EG is the edge set of G, and dt denotes the degree of an arbitrary vertex t in G. Soon after the innovation of the variable connectivity index, its various chemical applications have been reported in different papers. However, to the best of the authors’ knowledge, mathematical properties of the variable connectivity index, for γ>0, have not yet been discussed explicitly in any paper. The main purpose of the present paper is to fill this gap by studying this topological index in a mathematical point of view. More precisely, in this paper, we prove that the star graph has the minimum variable connectivity index among all trees of a fixed order n, where n≥4.

scholarly journals Computing Atom-Bond Connectivity (ABC4) index for Circumcoronene Series of Benzenoid

2013 ◽  
Vol 2 (1) ◽  
pp. 68-72 ◽  
Author(s):  
Mohammad Reza Farahani
Keyword(s):  
Connected Graph ◽  
Topological Index ◽  
Molecular Graph ◽  
Degree Of Vertex ◽  
Abc Index ◽  
Simple Connected Graph ◽  
Atom Bond

Let G=(V; E) be a simple connected graph. The sets of vertices and edges of G are denoted by V=V(G) and E=E (G), respectively. In such a simple molecular graph, vertices represent atoms and edges represent bonds. The Atom-Bond Connectivity (ABC) index is a topological index was defined as  where dv denotes degree of vertex v. In 2010, a new version of Atom-Bond Connectivity (ABC4) index was defined by M. Ghorbani et. al as  where and NG(u)={vV(G)|uvE(G)}. The goal of this paper is to compute the ABC4 index for Circumcoronene Series of Benzenoid

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

2013 ◽  
Vol 12 (10) ◽  
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.

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

2008 ◽  
Vol 4 (1) ◽  
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.

scholarly journals On Certain Aspects of Topological Indices

2021 ◽  
Vol 2021 ◽  
pp. 1-20
Author(s):  
Tanweer Ul Islam ◽  
Zeeshan Saleem Mufti ◽  
Aqsa Ameen ◽  
Muhammad Nauman Aslam ◽  
Ali Tabraiz
Keyword(s):  
Topological Index ◽  
Molecular Graph ◽  
Topological Indices ◽  
Connectivity Index ◽  
General Version ◽  
Zagreb Index ◽  
Harmonic Index ◽  
Degree Distance ◽  
Apex Graph ◽  
Structure Descriptor

A topological index, also known as connectivity index, is a molecular structure descriptor calculated from a molecular graph of a chemical compound which characterizes its topology. Various topological indices are categorized based on their degree, distance, and spectrum. In this study, we calculated and analyzed the degree-based topological indices such as first general Zagreb index M r G , geometric arithmetic index GA G , harmonic index H G , general version of harmonic index H r G , sum connectivity index λ G , general sum connectivity index λ r G , forgotten topological index F G , and many more for the Robertson apex graph. Additionally, we calculated the newly developed topological indices such as the AG 2 G and Sanskruti index for the Robertson apex graph G.

scholarly journals Topological Indices of Vitamin D3

2018 ◽  
Vol 7 (4) ◽  
pp. 6276
Author(s):  
Rajesh Kanna ◽  
Roopa S ◽  
PARASHIVAMURTHY H L
Keyword(s):  
Vitamin D3 ◽  
Topological Index ◽  
Topological Indices ◽  
Connectivity Index ◽  
First Zagreb Index ◽  
Zagreb Index ◽  
Second Zagreb Index ◽  
Augmented Zagreb Index ◽  
Abc Index ◽  
Ga Index

Graph theory has provided chemists with a variety of useful tools, such as topological indices. A topological index Top(G) of a graph G is a number with the property that for every graph H isomorphic to G, Top(H) = Top(G). In this paper, we compute ABC index, ABC4 index, Randi´c connectivity index, Sum connectivity index, GA index , GA5 index, First Zagreb index, Second Zagreb index, First Multiple Zagreb index, Second Multiple Zagreb index, Augmented Zagreb index, Harmonic index and Hyper Zagreb index, First Zagreb polynomial, Second Zagreb polynomial, Third Zagreb polynomial, Forgotten polynomials, Forgotten topological index and Symmetric division index of vitamin D3.

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