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.

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 Extremal trees with fixed degree sequence for atom-bond connectivity index

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 683-688 ◽  
Author(s):  
Rundan Xing ◽  
Bo Zhou
Keyword(s):  
Degree Sequence ◽  
Connectivity Index ◽  
Fixed Degree ◽  
Degree Of Vertex ◽  
Abc Index ◽  
Atom Bond

The atom-bond connectivity (ABC) index of a graph G is the sum of ?d(u)+d(v)?2/d(u)d(v) over all edges uv of G, where d(u) is the degree of vertex u in G. We characterize the extremal trees with fixed degree sequence that maximize and minimize the ABC index, respectively. We also provide algorithms to construct such trees.

scholarly journals On the maximum ABC index of bipartite graphs without pendent vertices

2020 ◽  
Vol 18 (1) ◽  
pp. 39-49 ◽  
Author(s):  
Zehui Shao ◽  
Pu Wu ◽  
Huiqin Jiang ◽  
S.M. Sheikholeslami ◽  
Shaohui Wang
Keyword(s):  
Bipartite Graph ◽  
Bipartite Graphs ◽  
Simple Graph ◽  
Connectivity Index ◽  
Degree Of Vertex ◽  
Abc Index ◽  
Pendent Vertices ◽  
Atom Bond

AbstractFor a simple graph G, the atom–bond connectivity index (ABC) of G is defined as ABC(G) = $\sum_{uv\in{}E(G)} \sqrt{\frac{d(u)+d(v)-2}{d(u)d(v)}},$where d(v) denotes the degree of vertex v of G. In this paper, we prove that for any bipartite graph G of order n ≥ 6, size 2n − 3 with δ(G) ≥ 2, $ABC(G)\leq{}\sqrt{2}(n-6)+2\sqrt{\frac{3(n-2)}{n-3}}+2,$and we characterize all extreme bipartite graphs.

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

scholarly journals On the Atom-Bond Connectivity index of cacti

Filomat ◽  
2014 ◽  
Vol 28 (8) ◽  
pp. 1711-1717 ◽  
Author(s):  
Hawei Dong ◽  
Xiaoxia Wu
Keyword(s):  
Connected Graph ◽  
Connectivity Index ◽  
Common Vertex ◽  
Sharp Bounds ◽  
Degree Of Vertex ◽  
Abc Index ◽  
Pendent Vertices ◽  
Atom Bond

The Atom-Bond Connectivity (ABC) index of a connected graph G is defined as ABC(G) = ?uv(E(G)?d(u)+d(v)-2/d(u)d(v), where d(u) is the degree of vertex u in G. A connected graph G is called a cactus if any two of its cycles have at most one common vertex. Denote by G0(n, r) the set of cacti with n vertices and r cycles and G1(n,p) the set of cacti with n vertices and p pendent vertices. In this paper, we give sharp bounds of the ABC index of cacti among G0(n,r) and G1(n,p) respectively, and characterize the corresponding extremal cacti.

Atom Bond Connectivity Index of Molecular Graphs of Alkynes and Cycloalkynes

2016 ◽  
Vol 13 (10) ◽  
pp. 6698-6706
Author(s):  
Mohanad A Mohammed ◽  
K. A Atan ◽  
A. M Khalaf ◽  
R Hasni ◽  
M. R. Md Said
Keyword(s):  
Molecular Structure ◽  
Connectivity Index ◽  
Molecular Graphs ◽  
Degree Of A Vertex ◽  
Abc Index ◽  
Atom Bond

The atom-bond connectivity (ABC) index is one of the recently most investigated degree based molecular structure descriptors that have applications in chemistry. For a graph G, the ABC index is defined as ABC(G) = <inline-formula> <mml:math display="block"> <mml:msub> <mml:mo>∑</mml:mo> <mml:mrow> <mml:mi>u</mml:mi><mml:mi>v</mml:mi><mml:mo>∈</mml:mo><mml:mi>E</mml:mi><mml:mo stretchy="false">(</mml:mo><mml:mi>G</mml:mi><mml:mo stretchy="false">)</mml:mo> </mml:mrow> </mml:msub> <mml:msqrt> <mml:mrow> <mml:mo stretchy="false">[</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>v</mml:mi> </mml:msub> <mml:mo>+</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>u</mml:mi> </mml:msub> <mml:mo>−</mml:mo><mml:mn>2</mml:mn><mml:mo stretchy="false">]</mml:mo><mml:mo>/</mml:mo><mml:mo stretchy="false">[</mml:mo><mml:msub> <mml:mi>d</mml:mi> <mml:mi>v</mml:mi> </mml:msub> <mml:mtext> </mml:mtext><mml:mo>·</mml:mo><mml:mtext> </mml:mtext><mml:msub> <mml:mi>d</mml:mi> <mml:mi>u</mml:mi> </mml:msub> <mml:mo stretchy="false">]</mml:mo><mml:mo>,</mml:mo> </mml:mrow> </mml:msqrt> </mml:math> </inline-formula> where du denotes the degree of a vertex u in G. In this paper, we establish the general formulas for the atom bond connectivity index of molecular graphs of alkynes and cycloalkynes.

scholarly journals The Atom-Bond Connectivity Index of Catacondensed Polyomino Graphs

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinsong Chen ◽  
Jianping Liu ◽  
Qiaoliang Li
Keyword(s):  
Upper Bound ◽  
Connectivity Index ◽  
Zigzag Chain ◽  
Extremal Graphs ◽  
Degree Of A Vertex ◽  
Abc Index ◽  
Atom Bond

LetG=(V,E)be a graph. The atom-bond connectivity (ABC) index is defined as the sum of weights((du+dv−2)/dudv)1/2over all edgesuvofG, wheredudenotes the degree of a vertexuofG. In this paper, we give the atom-bond connectivity index of the zigzag chain polyomino graphs. Meanwhile, we obtain the sharp upper bound on the atom-bond connectivity index of catacondensed polyomino graphs withhsquares and determine the corresponding extremal graphs.

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.

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.

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