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Topology-based optimization of handcuff graphs on 3D lattice
Title
Topology-based optimization of handcuff graphs on 3D lattice
Authors
No
;
Sungjong
;
Oh
;
Seungsang
;
Yoo
;
Hyungkee
Ewha Authors
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SCOPUS Author ID
유형기
Issue Date
2024
Journal Title
Physica Scripta
ISSN
0031-8949
Citation
Physica Scripta vol. 99, no. 1
Keywords
handcuff graph
;
lattice stick number
;
spatial graph
Publisher
Institute of Physics
Indexed
SCIE; SCOPUS
Document Type
Article
Abstract
In the field of macromolecular chemistry, handcuff-shaped catenanes and pretzelanes have a conformation consisting of two distinct loops and an edge connecting them. In spatial graph theory, this shape is referred to as a handcuff graph. One topological aspect of interest in these molecular structures involves determining the minimal number of monomers required to create them. In this paper, we focus on a handcuff graph situated in the cubic lattice, which we refer to as a lattice handcuff graph. We explicitly verify that constructing a lattice handcuff graph requires at least 14 lattice sticks, except for the two handcuff graphs: the trivial handcuff graph and the Hopf-linked handcuff graph. Mainly we employ the properly leveled lattice conformation argument, which was developed by the authors to find the lattice stick number of knot-shaped and link-shaped molecules. © 2023 IOP Publishing Ltd.
DOI
10.1088/1402-4896/ad1285
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