Dynamics of one-dimensional spin models under the line-graph operator

We investigate the application of line-graph operator to one-dimensional spin models with periodic boundary conditions. The spins (or interactions) in original structure become interactions spins) resulting structure. identify conditions which ensure that each new is stable, is, its configuration minimises internal energy. Then, making a correspondence between configurations and binary sequences, we propose model information growth evolution based on operator. Since this can generate frustrations newly formed chains, proposed such are immediately removed. Also, some cases, previously frustrated chains allowed recombine into stable chains. As result, obtain population whose dynamics studied using Monte Carlo simulations. Lastly, discuss potential applications areas research as combinatorics theoretical biology.