Random Models and Analyses for Chemical Graphs

Kouri, Tina M.; Pascua, Daniel; Mehta, Dinesh P.

doi:10.1142/s0129054115500161

Cited by 3 publications

(2 citation statements)

References 28 publications

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“…Some existing frameworks of random graphs that model chemical graphs can be found in the literatures [13,14]. There is a significant body of work done to representing chemical graphs as linear text strings (canonical label) and computing the structural similarity between two chemical graphs [15,16]. In line with literatures it is evident that for each chemical molecular graph, if a unique canonical labelling can be computed, then it would imply that efficient polynomial-time algorithms exists for GI problem.…”

Section: Distance/distancementioning

confidence: 89%

“Topological Stress” concept for quantizing chemical graph similarity scores

Ramraj,

Jaffer

2023

Preprint

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Graph Invariants can be used to infer molecular structural properties of graphs. In this work, a new distance metric between vertices of a graph is proposed to find the structural similarity between graphs. For this, a new distance matrix (known as IE matrix) is constructed based on the inverse Euclidean distance between graph vertices. This new representation directly depicts the skeletal structure of the vertices in the n-dimensional space. In this space, minimal distance between vertices implies high topological proximity between them. Based on IE matrix, a unique signature is generated for every graph which is used to find similarity between graphs. A new concept – “Topological Stress” is introduced that reveals the topological variation of a vertex with other vertices. Using this stress concept, similar topological stressed vertices between different graphs are identified and further explains the methylalkane interconversion reactions with the help of signature and dominant Eigen value. The entirety of the matrix is represented as a singularity which may serve as a unique molecular index (IEGPr) for chemical graphs. Similarity between graphs are calculated based on their corresponding IEGPr values. The resultant quantified similarity score lies between 0 and 1, referring value 1 for exact isomorphic. From the computational study, it is observed that IEGPr value is generally very low implying a low-value nomenclature of chemical graphs. Empirical study shows that the computational time required for the similarity identification procedure is scalable. From this it can be inferred that by improvising / reframing this measure a few application oriented Graph Matching problems can be tackled in polynomial time / near polynomial time.

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Section: Distance/distancementioning

confidence: 89%

“Topological Stress” concept for quantizing chemical graph similarity scores

Ramraj,

Jaffer

2023

Preprint

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“…In contrast to earlier works, where the canonical representation of a graph was typically defined to be the smallest graph isomorphic to it (in the lexicographic order), nauty introduced a notion which takes structural properties of the graph into account. The nauty tool has been applied in a wide range of applications which can be posed in terms of graph isomorphism, including graph drawing (Abelson et al 2002), identifying symmetries for SAT-solving (Aloul et al 2003), organic chemistry (Kouri et al 2015), and many others. It has been reported to apply to huge input graphs, including the report in (Royle 2015) on how it applies to a 76 million vertex graph.…”

Section: Introductionmentioning

confidence: 99%

Logic Programming with Graph Automorphism: Integrating`nauty`with Prolog (Tool Description)

Frank

Codish

2016

Theory and Practice of Logic Programming

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This paper presents the pl-nauty library, a Prolog interface to the nauty graph-automorphism tool. Adding the capabilities of nauty to Prolog combines the strength of the "generate and prune" approach that is commonly used in logic programming and constraint solving, with the ability to reduce symmetries while reasoning over graph objects. Moreover, it enables the integration of nauty in existing tool-chains, such as SAT-solvers or finite domain constraints compilers which exist for Prolog. The implementation consists of two components: pl-nauty, an interface connecting nauty's C library with Prolog, and pl-gtools, a Prolog framework integrating the software component of nauty, called gtools, with Prolog. The complete tool is available as a SWI-Prolog module. We provide a series of usage examples including two that apply to generate Ramsey graphs. This paper is under consideration for publication in TPLP.

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Two modified Zagreb indices for random structures

Shi

Gao

2021

Main Group Metal Chemistry

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Random structure plays an important role in the composition of compounds, and topological index is an important index to measure indirectly the properties of compounds. The Zagreb indices and its revised versions (or redefined versions) are frequently used chemical topological indices, which provide the theoretical basis for the determination of various physical-chemical properties of compounds. This article uses the tricks of probability theory to determine the reduced second Zagreb index and hyper-Zagreb index of two kinds of vital random graphs: G(n, p) and G(n, m).

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Random Models and Analyses for Chemical Graphs

Cited by 3 publications

References 28 publications

“Topological Stress” concept for quantizing chemical graph similarity scores

“Topological Stress” concept for quantizing chemical graph similarity scores

Logic Programming with Graph Automorphism: Integrating`nauty`with Prolog (Tool Description)

Two modified Zagreb indices for random structures

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Random Models and Analyses for Chemical Graphs

Cited by 3 publications

References 28 publications

“Topological Stress” concept for quantizing chemical graph similarity scores

“Topological Stress” concept for quantizing chemical graph similarity scores

Logic Programming with Graph Automorphism: Integratingnautywith Prolog (Tool Description)

Two modified Zagreb indices for random structures

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Product

Resources

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Logic Programming with Graph Automorphism: Integrating`nauty`with Prolog (Tool Description)