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