Exact Solution of Random Graphs for Cluster Fragmentation

We present the exact solution of a combinatorial fragmentation model and we show how it can be used as a touchstone for the fragmentation of atomic clusters. This model, random graphs (RG), also called mean field percolation, displays a phase transition. In this model, the clusters are solely described as connected entities called nodes. The connections, called bonds, can be active of broken. We have established the algebraic formulas of the probability of all the fragmentation channels. The results depend on the number of nodes and of the number of broken bonds. Using RG, we show example where information was deduced from fragmentation of systems consisting of finite sets of nodes.