A Study on Sprout Graphs
  Sprout graphs are finite directed graphs matured over a finite subset of the non-negative time line. A simple undirected connected graph on at least two vertices is required to construct an infant graph to mature from. The maxi-max arc-weight principle and the maxi-min arc-weight principle are introduced in the paper. These principles are used to determine the maximum and minimum maturity weight of a sprout graph. 
Johan Kok, Naduvath Sudev
math.CO