Maximum nullity and zero forcing number of graphs with rank at most 4

Let G be a simple graph with n vertices. The rank of G is the number of non-zero eigenvalues of its adjacency matrix and denoted by rank(G). In this paper, we show that if $ rank(G)=2 $, then zero forcing number and maximum nullity of G are equal to $ n-2 $. If $ rank(G)=3 $, then zero forcing number of G is equal to $ n-2 $ but maximum nullity of G is equal to $ n-3 $. Also, we introduce some graphs with rank of 4 such that these two parameters are equal