Periodic graphs and connectivity of the rational digital hyperplanes

Given a digital hyperplane of Zn defined by a double-inequality hi=1naixi<h+, we want to determine whether it is connected. The problem consists of computing the connectivity of a graph whose set of vertices is not finite. The classical algorithms of labelling are not deterministic in this framework but we can think of using the properties of the digital hyperplanes and in particular their periodicity to provide a deterministic method. It leads to introduce a special kind of graphs that we call periodic and whose properties allow to compute connective components of infinite size. It provides a deterministic algorithm determining whether a given rational digital hyperplane is connecte