A unified approach to the asymptotic topological indices of various lattices

•We present a unified approach to the asymptotic topological indices of various lattices.•We propose the topological indices per vertex problem for lattice systems.•The explicit asymptotic values of Laplacian energies for various lattices are obtained.•We deduce the Laplacian energies of many types of lattices are independent of various boundary conditions.

In this paper, we present a unified approach to the asymptotic topological indices of various lattices. Moreover, we propose the various topological indices per vertex problem for lattice systems and show that the various topological indices per vertex of lattices are independent of the toroidal, cylindrical, and free boundary conditions. Our result is a generalization of some earlier results.