The Granular Pebble Game

{\it The Pebble Game} represents a class of graph theoretic problems where pebbles (representing vertices) are constrained by bonds or physical contacts (edges). The pebble game also shares close correspondence with rigidity percolation transition in a variety of materials problems, where the evolution of rigidity in solids can be mapped to growth of network rigidity in a graph. Indeed, the class of materials known as topological or network glasses arose precisely from such an analysis in the context of chalcogenides and covalent glasses. Here we report a set of ultra-high precision experiments performed on a bidispersed set of photoelastic disks subjected to uni-axial compression. We analyse the formation of an amorphous granular solid from a loose granular pack under compression, as an exercise in the growth of rigidity in the granular contact network. We present preliminary results of our analysis to understand rigidity percolation in granular packs and their connection to the granular jamming transition.