Bounds on the connected forcing number of a graph
  In this paper, we study (zero) forcing sets which induce connected subgraphs of a graph. The minimum cardinality of such a set is called the connected forcing number of the graph. We provide sharp upper and lower bounds on the connected forcing number in terms of the minimum degree, maximum degree, girth, and order of the graph. 
Randy Davila, Michael Henning, Colton Magnant, and Ryan Pepper
math.CO