scholarly journals Some upper bounds for the atom–bond connectivity index of graphs

2012 ◽  
Vol 25 (7) ◽  
pp. 1077-1081 ◽  
Author(s):  
Jinsong Chen ◽  
Jianping Liu ◽  
Xiaofeng Guo
Keyword(s):  
Upper Bounds ◽  
Connectivity Index ◽  
Atom Bond

scholarly journals On atom-bond connectivity index

Filomat ◽  
2012 ◽  
Vol 26 (4) ◽  
pp. 733-738 ◽  
Author(s):  
Kinkar Das ◽  
Ivan Gutman ◽  
Boris Furtula
Keyword(s):  
Upper Bounds ◽  
Connectivity Index ◽  
Vertex Degree ◽  
Graph Invariant ◽  
Atom Bond

The atom-bond connectivity index (ABC) is a vertex-degree based graph invariant, put forward in the 1990s, having applications in chemistry. Let G = (V,E) be a graph, di the degree of its vertex i, and ij the edge connecting the vertices i and j. Then ABC = ?ij?E ?(di+dj?2)/(didj). Upper bounds and Nordhaus-Gaddum type results for ABC are established.

scholarly journals Some inequalities for the atom-bond connectivity index of graph operations

2011 ◽  
Vol 159 (13) ◽  
pp. 1323-1330 ◽  
Author(s):  
G.H. Fath-Tabar ◽  
B. Vaez-Zadeh ◽  
A.R. Ashrafi ◽  
A. Graovac
Keyword(s):  
Connectivity Index ◽  
Graph Operations ◽  
Atom Bond

scholarly journals On Atom-Bond Connectivity Index

2011 ◽  
Vol 66a ◽  
pp. 61 ◽  
Author(s):  
Zhou B. ◽  
Xing R.
Keyword(s):  
Connectivity Index ◽  
Atom Bond

scholarly journals More on comparison between first geometric-arithmetic index and atom-bond connectivity index

2016 ◽  
Vol 17 (1) ◽  
pp. 561 ◽  
Author(s):  
Zahid Raza ◽  
Akhlaq Ahmad Bhatti ◽  
Akbar Ali
Keyword(s):  
Connectivity Index ◽  
Atom Bond

scholarly journals Vertex-Based Topological Indices of Double and Strong Double Graph of Dutch Windmill Graph

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Muhammad Asad Ali ◽  
Muhammad Shoaib Sardar ◽  
Imran Siddique ◽  
Dalal Alrowaili
Keyword(s):  
Graph Theory ◽  
Chemical Properties ◽  
Topological Indices ◽  
Connectivity Index ◽  
Vaporization Enthalpy ◽  
Zagreb Index ◽  
Graph Operations ◽  
Big Graphs ◽  
Physical And Chemical ◽  
Atom Bond

A measurement of the molecular topology of graphs is known as a topological index, and several physical and chemical properties such as heat formation, boiling point, vaporization, enthalpy, and entropy are used to characterize them. Graph theory is useful in evaluating the relationship between various topological indices of some graphs derived by applying certain graph operations. Graph operations play an important role in many applications of graph theory because many big graphs can be obtained from small graphs. Here, we discuss two graph operations, i.e., double graph and strong double graph. In this article, we will compute the topological indices such as geometric arithmetic index GA , atom bond connectivity index ABC , forgotten index F , inverse sum indeg index ISI , general inverse sum indeg index ISI α , β , first multiplicative-Zagreb index PM 1   and second multiplicative-Zagreb index PM 2 , fifth geometric arithmetic index GA 5 , fourth atom bond connectivity index ABC 4 of double graph, and strong double graph of Dutch Windmill graph D 3 p .

scholarly journals On atom-bond connectivity index

2011 ◽  
Vol 511 (4-6) ◽  
pp. 452-454 ◽  
Author(s):  
Kinkar Ch. Das ◽  
Ivan Gutman ◽  
Boris Furtula
Keyword(s):  
Connectivity Index ◽  
Atom Bond

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.

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