  The geometric properties of a lattice can have profound consequences on its
band spectrum. For example, symmetry constraints and geometric frustration can
give rise to topologicially nontrivial and dispersionless bands, respectively.
Line-graph lattices are a perfect example of both of these features: their
lowest energy bands are perfectly flat, and here we develop a formalism to
connect some of their geometric properties with the presence or absence of
fragile topology in their flat bands. This theoretical work will enable
experimental studies of fragile topology in several types of line-graph
lattices, most naturally suited to superconducting circuits.
