Isomer Enumeration of Alkenes and Aliphatic Cyclopropane Derivatives

Yeh, Chin-yah

doi:10.1021/ci960008l

Cited by 7 publications

(2 citation statements)

References 10 publications

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“…Mathematically recount of alkenes with geometric isomerism due to a double bond was taken into consideration [5]. Further the mathematical relationship between the number of isomers of alkenes and alkynes was established from the enumeration of isomers of alkenes and alkynes [2].Computerised isomer Enumeration of the Alkane Series was presented [1] and an algorithm to enumerate the isomers of eighteen carbon atoms alkane series was implemented in the Object Oriented programing language-C++.…”

Section: Related Workmentioning

confidence: 99%

Development of an Efficient Algorithm to Enumerate the Number of Constitutional Isomers of Alkyne Series

KumarChouhan¹,

Sangal²

2012

IJCA

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Computerized Enumeration of alkane's isomers has long been a topic of interest to the researchers. The double bond carbon content and triple bond carbon content isomers were mostly neglected for many decades by the researchers and claimed in the literature that there is no simple algorithm for these problems. In this paper an efficient and simple algorithm has been proposed to count the number of constitutional isomers of alkynes series. By using this recursive algorithm the resulting computation of number of isomers for alkynes with any number of carbon contents [limited to system specifications] are easily enumerated. Further the time complexity of the proposed algorithm has also been investigated. The algorithm has been implemented using object oriented programming language-Java.

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Section: Related Workmentioning

confidence: 99%

Development of an Efficient Algorithm to Enumerate the Number of Constitutional Isomers of Alkyne Series

KumarChouhan¹,

Sangal²

2012

IJCA

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“…Following the enumerating theories and techniques mentioned above, lots of treelike molecules beyond alkanes have also been discussed, e.g. : tree-like polyhexes (with asymptotic analysis) [29]; phenylenes [30]; tree-like polymers [31]; radicals, monoalcohols, glycols and esters [32]; aliphatic cyclopropane derivatives [33]; etc. As regards mathematical aspects, a large number of trees or tree-like graphs with some specific requirements were also discussed; we refer the reader to, for example, [34]- [42] and the references cited therein.…”

Section: Introductionmentioning

confidence: 99%

Enumerating tree-like polyphenyl isomers

Deng¹,

Qian²,

Zhang³

2012

J. Stat. Mech.

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Enumeration of molecules is one of the fundamental problems in bioinformatics and plays an important role in drug discovery, experimental structure elucidation (e.g., by using NMR or mass spectrometry), molecular design and virtual library construction. We consider the enumeration of tree-like polyphenyls (C 6n H 4n+2 ). For this purpose, we define two generating functions T (x) and R(x) involving the numbers t n and r n of tree-like polyphenyls (TLpolyphenyls) and monosubstituted tree-like polyphenyls (MTL-polyphenyls), respectively. By characterizing the symmetry groups with respect to TLpolyphenyls and MTL-polyphenyls, we establish two functional equations for these two generating functions. This yields for the first time an efficient recursion formula for calculating the numbers t n and r n . The two functional equations are also the fundamentals for analyzing their asymptotic behaviors, from which we derive the precise asymptotic values for both r n and t n . The resulting asymptotic values are shown to fit well to the numerical results obtained by using our recursion formula. Finally, we give an explicit enumerating expression for TLpolyphenyls of a particular type: the linear polyphenyls.

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