Abstarct: It is known that zero forcing number is an upper bound for the maximum nullity of a graph. Computing zero forcing number, total forcing number, and connected forcing number of graphs lies in the class of NP-hard problems. The graphs with zero forcing number 1 and 2 are respectively the paths and the graphs of 2-parallel paths. In this thesis, we first define the graphs of k-parallel paths and then introduce some upper bounds for zero forcing number and total forcing number of the graphs of k-parallel paths. Next, we characterize the graphs with maximum degree at most three and zero forcing number three and then as a conclusion, we exactly find the graphs with maximum degree at most three having zero forcing number and maximum nullity at most three. Moreover we characterize the graphs with total forcing number two as well as the graphs with connected forcing number two.