Abstract
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.
Funder
National Research Foundation of Korea
Subject
Condensed Matter Physics,Mathematical Physics,Atomic and Molecular Physics, and Optics
Reference27 articles.
1. An efficient approach for solving the HP protein folding problem based on UEGO;García-Martínez;J. Math. Chem.,2015
2. Hybrid method to solve HP model on 3D lattice and to probe protein stability upon amino acid mutations;Guo;BMC Syst. Biol.,2017
3. Protein 3D HP model folding simulation using a hybrid of genetic algorithm and particle swarm optimization;Lin;Int. J. Fuzzy Syst.,2011
4. Stick index of knots and links in the cubic lattice;Adams;J. Knot Theory Ramifications,2012
5. Characterizing polygons in R3;Calvo;Contemp. Math.,2002