Topological densities of periodic graphs

Abstract

Abstract We propose a new method to calculate topological densities of periodic graphs based on the concept of layer-by-layer growth. Topological density is expressed in terms of metric characteristics: the volume of the fundamental domain and the volume of the growth polytope of the graph. Our method is universal (works for all d-periodic graphs) and is easily automated. As examples, we calculate topological densities of all 20 plane 2-uniform graphs and 14 carbon allotrope modifications.