Explosion in a growth model with cooperative interaction on an infinite graph

In this paper we study a probabilistic model for the asymptotic behavior of particles adsorption process on an infinite graph. Adsorption may be defined as the process of accumulation of a substance on a surface. The adsorption process can be classified into two types: Physical Adsorption or chemical adsorption. The physical adsorption happen when molecules or atoms adhere to the adsorbent surface by intermolecular interactions while in chemical adsorption there are chemical attraction forces or chemical bond between substance and surface [3].