G-Strongly Positive Scripts and Critical Configurations of Chip Firing Games on Digraphs

We show a collection of scripts, called G-strongly positive scripts, which is used to recognize critical configurations of a CFG (chip firing game) on a multi-digraph with a global sink. Moreover, an algorithm for finding the minimum G-strongly positive script is also given. From that we generalize a very recent result by Aval et.al which prove the non-stableness of configurations obtained from a critical configuration by firing inversely any non-empty multi-subset of vertices for digraphs.