Codes for distributed storage from 3-regular graphs
  This paper considers distributed storage systems (DSSs) from a graph theoretic perspective. A DSS is constructed by means of the path decomposition of a 3- regular graph into P4 paths. The paths represent the disks of the DSS and the edges of the graph act as the blocks of storage. We deduce the properties of the DSS from a related graph and show their optimality. 
Shuhong Gao, Fiona Knoll, Felice Manganiello and Gretchen Matthews
cs.IT math.CO math.IT