scholarly journals On the generalized ABC index of graphs

2021 ◽  
Vol 87 (01) ◽  
pp. 147-169
Author(s):  
Kinkar Chandra Das ◽  
◽  
José Rodrı́guez ◽  
José Sigarreta
Keyword(s):  
2019 ◽  
Vol 39 (4) ◽  
pp. 450-460
Author(s):  
Lucas M. A. Goossens ◽  
Marcel F. Jonker ◽  
Maureen P. M. H. Rutten-van Mölken ◽  
Melinde R. S. Boland ◽  
Annerika H. M. Slok ◽  
...  

Background In discrete-choice experiments (DCEs), choice alternatives are described by attributes. The importance of each attribute can be quantified by analyzing respondents’ choices. Estimates are valid only if alternatives are defined comprehensively, but choice tasks can become too difficult for respondents if too many attributes are included. Several solutions for this dilemma have been proposed, but these have practical or theoretical drawbacks and cannot be applied in all settings. The objective of the current article is to demonstrate an alternative solution, the fold-in, fold-out approach (FiFo). We use a motivating example, the ABC Index for burden of disease in chronic obstructive pulmonary disease (COPD). Methods Under FiFo, all attributes are part of all choice sets, but they are grouped into domains. These are either folded in (all attributes have the same level) or folded out (levels may differ). FiFo was applied to the valuation of the ABC Index, which included 15 attributes. The data were analyzed in Bayesian mixed logit regression, with additional parameters to account for increased complexity in folded-out questionnaires and potential differences in weight due to the folding status of domains. As a comparison, a model without the additional parameters was estimated. Results Folding out domains led to increased choice complexity for respondents. It also gave domains more weight than when it was folded in. The more complex regression model had a better fit to the data than the simpler model. Not accounting for choice complexity in the models resulted in a substantially different ABC Index. Conclusion Using a combination of folded-in and folded-out attributes is a feasible approach for conducting DCEs with many attributes.


2016 ◽  
Vol 13 (10) ◽  
pp. 6698-6706
Author(s):  
Mohanad A Mohammed ◽  
K. A Atan ◽  
A. M Khalaf ◽  
R Hasni ◽  
M. R. Md Said

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.


2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Jinsong Chen ◽  
Jianping Liu ◽  
Qiaoliang Li

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.


2014 ◽  
Vol 79 (5) ◽  
pp. 557-563 ◽  
Author(s):  
Ivan Gutman ◽  
Lingping Zhong ◽  
Kexiang Xu

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.


2016 ◽  
Vol 12 (8) ◽  
pp. 301-305
Author(s):  
Mohammad Reza Farahani

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.


2018 ◽  
Vol 338 ◽  
pp. 221-230 ◽  
Author(s):  
Wenshui Lin ◽  
Jianfeng Chen ◽  
Zhixi Wu ◽  
Darko Dimitrov ◽  
Linshan Huang

2017 ◽  
Vol 56 (2) ◽  
pp. 568-582 ◽  
Author(s):  
Xiu-Mei Zhang ◽  
Yu-Qin Sun ◽  
Hua Wang ◽  
Xiao-Dong Zhang

2008 ◽  
Vol 3 ◽  
pp. 62
Author(s):  
M. Hasegawa ◽  
M. Mabuchi ◽  
H. Takeyama
Keyword(s):  

Filomat ◽  
2013 ◽  
Vol 27 (6) ◽  
pp. 1075-1083 ◽  
Author(s):  
Ivan Gutman ◽  
Boris Furtula ◽  
Mohammad Ahmadi ◽  
Seyyed Hosseini ◽  
Salehi Nowbandegani ◽  
...  
Keyword(s):  

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