The square G of a graph G is the graph obtained from G by adding an edge between every pair of vertices having a common neighbor. A proper coloring of G is also called a 2-distance coloring of G. The maximum average degree Mad(G) of a graph G is the maximum among the average degrees of the subgraphs of G, i.e. Mad(G) = max { 2|E(H)| V (H) |H ⊆ G } . Graphs with bounded maximum average degree ar...

In recent years, new experimental techniques opened way to creation and study of high energy (Rydberg) states in atoms. These states are described by approximate hydrogenic wave functions with very large principal quantum numbers. Some new effects, as the dynamical localization and the dynamical chaos, have attracted considerable interest. Explanation of these phenomena uses classical equations...