Techniques for determining equality of the maximum nullity and the zero forcing number of a graph

It is known that the zero forcing number of a graph an upper bound for maximum nullity (see [AIM Minimum Rank - Special Graphs Work Group (F. Barioli, W. Barrett, S. Butler, Cioab$\breve{\text{a}}$, D. Cvetkovi$\acute{\text{c}}$, Fallat, C. Godsil, Haemers, L. Hogben, R. Mikkelson, Narayan, O. Pryporova, I. Sciriha, So, Stevanovi$\acute{\text{c}}$, H. van der Holst, K. Vander Meulen, and A. Wangsness). Linear Algebra Appl., 428(7):1628--1648, 2008]). In this paper, we search characteristics guarantee are same by studying variety parameters give lower bounds on graph. Inparticular, introduce new parameter which acts as As result, show Aztec Diamond graph's same. Other considered Colin de Verdiére type vertex connectivity. We also use matrices, such divisor matrix equitable partition adjacency graph, to establish matrix.