Mathematical Basis of Ring-Finding Algorithms in CIDS

Plotkin, Morris

doi:10.1021/c160040a013

Cited by 47 publications

(34 citation statements)

References 6 publications

(14 reference statements)

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“…The cycles (C) of a connected graph form a vector space called the cycle space [41]. Let E be the number of edges and V the number of vertices.…”

Section: Appendix a The Basics Of Ring Perceptionmentioning

confidence: 99%

“…For example for adamantane, μ = 12 − 10+1 = 3, meaning that any three of the elementary rings with length 6 can provide an SSSR. Therefore the concept of K-rings [41], although called relevant rings [40] were introduced, which are those elementary rings, which appear in one of the SSSR of the graph. The relevant rings are basically elementary rings, which cannot be formed by the direct sum of smaller rings, but some of them can be created by the direct sum of rings of the same size.…”

Section: Appendix a The Basics Of Ring Perceptionmentioning

confidence: 99%

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Ring structure analysis of ethanol–water mixtures

Gereben

2015

Journal of Molecular Liquids

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“…The cycles (C) of a connected graph form a vector space called the cycle space [41]. Let E be the number of edges and V the number of vertices.…”

Section: Appendix a The Basics Of Ring Perceptionmentioning

confidence: 99%

Section: Appendix a The Basics Of Ring Perceptionmentioning

confidence: 99%

Ring structure analysis of ethanol–water mixtures

Gereben

2015

Journal of Molecular Liquids

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“…A cycle is relevant if it cannot be written as ⊕-sum of shorter cycles. Equivalently, a cycle is relevant if it is contained in at least one minimum cycle basis [45,56]. We write R(G) for the set of relevant cycles.…”

Section: Preliminariesmentioning

confidence: 99%

Counterexamples in Chemical Ring Perception

Berger

Flamm

Gleiss

et al. 2004

J. Chem. Inf. Comput. Sci.

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Abstract. Ring information is a large part of the structural topology used to identify and characterize molecular structures. It is hence of crucial importance to obtain this information for a variety of tasks in computational chemistry. Many different approaches for "ring perception", i.e., the extraction of cycles from a molecular graph, have been described. The chemistry literature on this topic, however, reports a surprisingly large number of incorrect statements about the properties of chemically relevant ring sets and, in particular, about the mutual relationships of different sets of cycles in a graph. In part these problems seem to have arisen from a sometimes rather idiosyncratic terminology for notions that are fairly standard in graph theory. In this contribution we translate the definitions of concepts such as the Smallest Set of Smallest Rings, Essential Set of Essential Rings, Extended Set of Smallest Rings, Set of Smallest Cycles at Edges, Set of Elementary Rings, K-rings, and β-rings into a more widely-used mathematical language. We then outline the basic properties of different cycle sets and provide numerous counterexamples to incorrect claims in the published literature. These counterexamples may have a serious practical impact because at least some of them are molecular graphs of well-known molecules. As a consequence, we propose a catalogue of desirable properties for chemically useful sets of rings.

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“…A cycle C is relevant if it cannot be represented as an È-sum of shorter cycles [10]. Equivalently, a cycle is relevant if and only if it is contained in a minimum cycle basis [14].…”

Section: Preliminariesmentioning

confidence: 99%